1  General Information

1.1 Unit Conversions¹

(SAWE Weight Engineers Handbook 1976; Aeronautical Vestpocket Handbook 1991; “Online Conversion - Convert Just about Anything to Anything Else” n.d.; “1976 Standard Atmosphere Calculator” n.d.)

Prefix Multipliers

Exponent	Prefix	Abbreviation
1018	exa	E
1015	peta	P
1012	tera	T
109	giga	G
106	mega	M
103	kilo	k
102	hecto	h
10	deka	da
10-1	deci	d
10-2	centi	c
10-3	milli	m
10-6	micro	\(\mu\)
10-9	nano	n
10-12	pico	p
10-15	femto	f
10-18	atto	a

	Multiply	by	To Obtain
Angles	circles	1	circumferences
	circles	12	signs
	circles	21,600	minutes
	circles	2\(\pi\)	radians
	circles	360	degrees
	degrees	0.011 11	quadrants
	degrees	3600	seconds
	degrees	60	minutes
	mils (Army)	0.056 25	degrees
	mils (Navy)	0.057 29	degrees
	quadrants	90	degrees
	radians	57.2958	degrees
	revolutions	360	degrees
2	sphere	4\(\pi\)	steradians
Angular Acceleration	rev/min2	0.001 745	rad/sec2
Angular Velocity	cycles/sec	6.2814	rads/sec
	rads/sec	0.1592	rev/sec (cycles/sec)
	rads/sec	9.549	rpm
	rad/sec	57.296	deg/sec
	rpm	0.016 67	rev/sec
Area	acres	43,560	ft2
	ares	100	m2
	barn	10-28	m2
	centares	1	m2
	circular mils	7.854 x 10-7	in2
	cm2	100	mm2
	ft2	144	in2
	ft2	0.092 903 04	m2
	in2	6.452	cm2
	in2	106	mils2
	m2	10.76	ft2
	section	2,589,988.1	m2
	st. mile2	27,780,000	ft2
	st. mile2	2.590	km2
	township	93,239,572	m2
	yd2	9	ft2
	yd2	0.8361	m2
Density	grams/cm3	0.036 13	pounds/in3
	grams/cm3	62.43	pounds/ft3
	kg/m3	16.018 463	pounds/ft3
	slugs/ft3	515.4	kg/m3
	pounds/in3	1728	pounds/ft3
	slugs/ft3	1.94	grams/cm3
Electrical Quantities	amperes	0.1	abamperes
	amperes	1.0365x10-5	faradays/sec
	amperes	2.998x109	statamperes
	amperes.cicmil	1.973x105	amperes/cm2
	ampere-hours	3,600	coulombs
	ampere-hours	1.079x1013	statcoulombs
	ampere turn/cm	1.257	gilberts/cm
	ampere turn/cm	1.257	oersteds
	coulombs	0.1	abcoulombs
	coulombs	6.243x1018	electronic charges
	coulombs	1.037x10-5	faradays
	coulombs	2.998x109	statcoulombs
	faradays	26.8	ampere-hours
	farads	10-9	abfarads
	farads	106	microfarads
	farads	8.986x1011	statfarads
	gausses	1	maxwells/cm2
	gausses	6.452	lines/in2
	gilberts	0.7958	ampere turns
	henries	109	abhenries
	henries	1.113x10-12	stathenries
	maxwells	1	lines
	oersteds	2.998x1010	statoersteds
	ohms	109	abohms
	ohms	1.113x1012	statohms
	ohm-cm	6.015x106	circ mil-ohms/ft
	volts	108	abvolts
	volts	0.003 336	statvolts
Energy & Work	Btu	1.055x1010	ergs
	Btu	1055.1	Joules (N-m)
	Btu	2.9302x10-4	kilowatt-hours
	Btu	251.99	calories (gram)
	Btu	778.03	foot-pounds
	calories	4.1868	watt-seconds
	calories	3.088	foot-pounds
	electron volt	1.519x10-22	Btu
	ergs	1	dyne-centimeters
	ergs	7.376x108	foot-pounds
	foot-pounds	1.3558	Joules (N-m)**
	foot-pounds	3.766x10-7	kilowatt-hours
	foot-pounds	5.051x10-7	horsepower-hours
	hp-hours	0.7457	kilowatt-hours
	hp-hours	2546.1	Btu
	Joules	0.238 89	calories
	Joules	1	Newton-meters
	Joules	1	watt-seconds
	Joules	107	ergs
	kilowatt-hours	3.6x106	Joules
	thermies	4.1868x106	Joules
	watt-seconds	0.737 56	foot-pounds
Force3	dynes	3.597x10-5	ounces
	kilograms-force	9.806 65	Newtons
	kiloponds	9.806 65	Newtons
	kip (kilopound-force)	4,448.221	Newtons
	Newtons	0.224 808 931	pounds
	Newtons	100,000	dynes
	ounces	20	pennyweights
	ounces (troy)	480	grains
Fuel4	gal	5.8	lbs (U.S. AV gas)
	gal	7.5	lbs ( U.S. oil)
	Liter (jet A)	0.812	kilograms
	Liter (jet A)	1.794	pounds
Illumination	candles	1	lumens/steradian
	candles/cm2	\(\pi\)	lamberts
	candlepower	12.566	lumens
	foot-candles	1	lumens/ft2
	foot-candles	10.764	lux
	foot-lamberts	1	lumen/ft2
	lamberts	295.72	candles/ft2
	lamberts	929.03	lumens/ft2
	lumens	0.001 496	watts
	lumens/in2	1	fots
	lumens/m2	1	lux
	lux	1	meter-candles
	lux	0.0001	fots
	meter-candles	1	lumens/m2
	millilamberts	0.2957	candles/ft2
	millilamberts	0.929	foot-lamberts
	milliphots	0.929	foot-candles
	milliphots	0.929	lumens/ft2
	milliphots	10	meter-candles
Length	ångströms	10-10	meters
	astronomical units	1.496x1011	meters
	cable lengths	120	fathoms
	caliber	0.01	inches
	cubit	0.4572	meters
	fermi	10-15	meters
	fathoms	6	feet
	feet	12	inches
5	feet	0.3048	meters
	furlongs	40	rods
	hands	4	inches
	inches	2.54	cm
	kilometers	3281	feet
	kilometers	0.539 96	nautical miles
	leagues (U.S.)	3	nautical miles
	light years	5.88x1012	statute miles
	links (engnr’s)	12	inches
	links (srvyr’s)	7.92	inches
	meters	3.280 84	feet
	meters	39.370 079	inches
	microns	10-6	meters
	mils	10-3	inches
	nautical miles	1.150 78	statute miles
6	nautical miles	1,852	meters
	nautical miles	6,076.115 486	feet
	paces	0.762	meters
	parsec	1.9163x1013	statute miles
	perch	5.0292	meters
	pica (printers)	0.004 217 5176	meters
	point (printers)	0.000 351 4598	meters
	pole (=rod)	5.0292	meters
	skein	109.728	meters
	statute miles	5,280	feet
	statute miles	1.609 344	kilometers
	statute miles	8	furlongs
	yards	3	feet
Linear Acceleration	feet/sec2	1.097 28	kilometers/hr/sec
	feet/sec2	0.3048	meters/sec2
	feet/sec2	0.6818	mph/sec
	g	32.174 049	feet/sec2
	g	9.806 65	meters/sec2
	gals (Galileo)	0.01	meters/sec2
	knots/sec	1.6878	feet/sec2
	meters/sec2	3.6	kilometers/hr/sec
	mph/sec	0.447	meters/sec2
	mph/sec	1.609	kilometers/hr/sec
Mass	carats	200	milligrams
	grams	0.035 274	ounces
	grains	6.479 891x10-5	kilograms
	hundredweight (long or Imperial)	50.80	kilograms
	hundredweight (short)	45.359 237	kilograms
	kilograms	0.068 52	slugs
	kilograms	6.024x1026	atomic mass units
	kilograms	2.2046	pounds
	ounces (avd)	28.349 523 125	grams
	ounces (troy)	31.103 4768	grams
	pounds (mass)	1	pounds (force)
	pounds (mass)	0.453 592 37	kilograms
	pounds (mass)	0.031 081	slugs
	scruples (apoth)	0.001 295 9782	kilograms
	slugs	32.174	pounds
	slugs	14.594	kilograms
	tons (long)	1016.047	kilograms
	tons (assay)	0.029 16	kilograms
	tons (metric)	1000	kilograms
	tons (short)	907.1847	kilograms
Moments of Inertia	gram-cm2	0.737x10-7	slug-ft2
	pound-ft2	0.031 081	slug-ft2
	slug-in2	0.006 9444	slug-ft2
	slug-ft2	1.3546	kg-m2
	slug-ft2	32.174	pound-ft2
	slug-ft2	12.00	pound-inch-sec2
	slug-ft2	192.00	ounce-inch-sec2
Power	btu/min	0.017 58	kilowatts
	calories(kg)/min	3087.46	foot-pounds/min
	ergs/sec	7.376x10-8	foot-pounds/sec
	ft(lbs)/min	2.260x10-5	kilowatts
	ft(lbs)/sec	0.077 12	btu/min
	ft(lbs)/sec	1.356	watts
	horsepower	550	ft(lb)/sec
	horsepower	33,000	ft(lbs)/min
	horsepower	10.69	calories (kg)/min
	horsepower	745.7	watts
	horsepower (metric)	735.5	watts
	horsepower	1.1014	horsepower (metric)
	kilowatts	1.341	horsepower
	watts	107	ergs/sec
	watts	1	Joules/sec
Pressure	atmospheres	14.696	pounds/in2
	atmospheres	29.92	inches of Hg
	atmospheres	760	mm of Hg
	bars	106	dynes/cm2
	bars	29.52	inches of Hg
	barye	0.1	Newtons/m2
	dynes/cm2	10	Newtons/m2
	inches of H2O	5.202 37	pound/ft2
	inches of Hg	70.726 19	pounds/ft2
	inches of Hg	0.491 154	pounds/in2
	inches of Hg	13.595	inches of H2O
	kiloPascals	100	bars
	hectoPascals	1	millibars
	millibars	0.029 53	inches of Hg
	mm of Hg	0.019 337	pounds/in2
	mm of Hg	133.32	Newtons/m2
	Pascals	1	Newton/m2
	pieze	1000	Newtons/m2
	pounds/ft2	0.014 14	inches of Hg
	pounds/ft2	47.88	Newtons/m2
	pounds/in2	2.036	inches of Hg
	pounds/in2	27.681	inches of H2O
	pounds/in2	6894.757 28	Pascal
	torrs	133.32	Newtons/m2
Temperature	Kelvin	Celsius + 273.15
	Rankine	Fahrenheit + 459.67
	Celsius	(Fahrenheit - 32) * 5/9
	Fahrenheit	(9/5 * Celsius) + 32
Time	days (solar)	24	hours
	days (sidereal)	23.934	hours
	days (solar)	1.0027	days (sidereal)
	hours	60	minutes
	minutes	60	seconds
	months (sidereal)	27d + 7hr + 43min + 11.47sec
	months (lunar)	29d + 12hr + 44min + 2.78sec
	year	365.242 198 79	days
Torque	foot-pounds	1.3558	Newton-meters
	foot-pounds	0.1383	kilogram-meters
	ounce-inches	72.008	gram-centimeters
	pound-inches	1129800	dyne-centimeters
Velocity	inches/sec	0.0254	meters/sec
	km/hr	0.621 371	mph
	km/hr	0.9113	feet/sec
	knots	1.687 81	feet/sec
	knots (kts)	1.150 78	mph
	knots (kts)	1.852	km/hr
	knots (kts)	0.514 44	meters/sec
	meters/sec	3.281	ft/sec
	meters/sec	3.6	km/hr
	meters/sec	196.85	feet/min
	mph	1.466 667	feet/sec
Viscosity	centistokes	10-6	m2/sec
	ft2/sec	0.0929	m2/sec
	pound sec/ ft2	47.880 258	Newton secs/m2
	poise	0.1	Newton secs/m2
	rhe	10	m2/Newton second
Volume	acre-feet	43,560	ft3
	acre-feet	1,233	m3
	acre-feet	3.259x105	gals (U.S.)
	barrels	31.5	gals (U.S.)
	board-feet	144	in3
	bushels	1.244	ft3
	bushels	32	quarts (dry)
	bushels	4	pecks
	cm3	0.001	liters
	cm3	0.033 81	fluid ounces
	cm3	0.061 02	in3
	cord-feet	4x4x1	ft3
	cords	128	ft3
	cups	0.5	pints (liquid)
	dram (fluid)	3.696 69x10-6	m3
	ft3	0.028 3167	m3
	ft3	1728	in3
	ft3	28.32	liters
	ft3	7.481	gals (U.S.)
	gals (Imperial)	1.2009	gals (U.S.)
	gals (Imperial)	277.42	in3
	gals (U.K.)	4546.1	cm3
	gals (U.S.)	231	in3
	gals (U.S.)	0.003 785	m3
	gals (U.S.)	3.785	liters
	gals (U.S.)	4	quarts (liquid)
	gals (U.S.)	0.023 8095	barrels (U.S.)
	gills	7.219	in3
	hogshead	2	barrels
	in3	16.39	cm3
	liters	0.028 38	bushels
	liters	0.9081	quarts (dry)
	liters	1.057	quarts (liquid)
	liters	1000	cm3
	liters	61.03	in3
	m3	1.308	yd3
	m3	1000	liters
	m3	264.2	gals (U.S.)
	m3	35.314 667	ft3
	mil-feet (circ.)	0.000 1545	cm3
	ounces (U.K.)	28.413	cm3
	ounces (U.S.)	29.574	cm3
	pecks	8	quarts (dry)
	pecks	8.81	liters
	perches	0.7008	m3
	perches	24.75	ft3
	pints (dry)	33.60	in3
	pints (liquid)	28.88	in3
	pints (liquid)	4	gals
	quarts (dry)	1.164	quarts (liquid)
	quarts	2	pints
	register tons	100	ft3
	shipping ton (U.S.)	40	ft3
	shipping ton (Br.)	42	ft3
	steres	1000	liters
	tablespoons	0.0625	cups
	teaspoons	0.3333	tablespoons

1.2 Greek Alphabet

Uppercase	LaTeX Command	Lowercase	LaTeX Command	Name	Say
\(Α\)	Α	\(\alpha\)	\alpha	Alpha	æl-fə
\(Β\)	Β	\(\beta\)	\beta	Beta	bei-tə
\(\Gamma\) or \(\varGamma\)	\Gamma or \varGamma	\(\gamma\)	\gamma	Gamma	gæ-mə
\(\Delta\) or \(\varDelta\)	\Delta or \varDelta	\(\delta\)	\delta	Delta	del-tə
\(Ε\)	Ε	\(\epsilon\) or \(\varepsilon\)	\epsilon or \varepsilon	Epsilon	eps-ill-aan
\(Ζ\)	Ζ	\(\zeta\)	\zeta	Zeta	zei-tə
\(Η\)	Η	\(\eta\)	\eta	Eta	ei-tə
\(\Theta\) or \(\varTheta\)	\Theta or \varTheta	\(\theta\) or \(\vartheta\)	\theta or \vartheta	Theta	thei-tə
\(Ι\)	Ι	\(\iota\)	\iota	Iota	aai-oh-tə
\(Κ\)	Κ	\(\kappa\) or \(\varkappa\)	\kappa or \varkappa	Kappa	kæ-pə
\(\Lambda\) or \(\varLambda\)	\Lambda or \varLambda	\(\lambda\)	\lambda	Lambda	læm-də
\(M\)	M	\(\mu\)	\mu	Mu	myoo
\(Ν\)	Ν	\(\nu\)	\nu	Nu	nyoo
\(\Xi\) or \(\varXi\)	\Xi or \varXi	\(\xi\)	\xi	Xi	ksaai
\(Ο\)	Ο	\(ο\)	ο	Omicron	oh-mə-kraan
\(\Pi\) or \(\varPi\)	\Pi or \varPi	\(\pi\) or \(\varpi\)	\pi or \varpi	Pi	paai
\(P\)	P	\(\rho\) or \(\varrho\)	\rho or \varrho	Rho	roh
\(\Sigma\) or \(\varSigma\)	\Sigma or \varSigma	\(\sigma\) or \(\varsigma\)	\sigma or \varsigma	Sigma	sig-mə
\(Τ\)	Τ	\(\tau\)	\tau	Tau	taa’u
\(\Upsilon\) or \(\varUpsilon\)	\Upsilon or \varUpsilon	\(\upsilon\)	\upsilon	Upsilon	oops-ill-on
\(\Phi\) or \(\varPhi\)	\Phi or \varPhi	\(\phi\) or \(\varphi\)	\phi or \varphi	Phi	faai
\(Χ\)	Χ	\(\chi\)	\chi	Chi	kaai
\(\Psi\) or \(\varPsi\)	\Psi or \varPsi	\(\psi\)	\psi	Psi	psaai
\(\Omega\) or \(\varOmega\)	\Omega or \varOmega	\(\omega\)	\omega	Omega	oh-meg-ə

1.3 Greek Symbols Used for Aircraft

Symbol	Used For
\(\alpha\)	angle of attack (degrees or radians)
\(\alpha_{\tau}\)	tail angle of attack
\(\beta\)	angle of sideslip (degrees)
\(\gamma\)	flight path angle relative to horizontal
\(\gamma\)	specific heat ratio (1.4 for air)
\(\delta\)	relative pressure ratio ( \(\frac{P_a}{P_0}\))
\(\delta_a\)	aileron deflection angle
\(\delta_r\)	rudder deflection angle
\(\delta_e\)	elevator deflection angle
\(\varepsilon\)	downwash angle at tail (degrees)
\(\zeta\)	damping ratio
\(\eta\)	efficiency
\(\theta\)	body axis/pitch angle
\(\theta\)	relative temperature ratio, \(T_a / T_0\)
\(\iota\)	angle of incidence
\(\iota_F\)	thrust angle of incidence
\(\iota_T\)*	horizontal tail angle of incidence
\(\lambda\)	pressure lag constant
\(\Lambda\)	wing sweep angle
\(\mu\)	coefficient of absolute viscosity =\(\rho \nu\)
\(\mu\)	Mach cone angle
\(\nu\)	kinematic viscosity =\(\mu / g\)
\(\pi\)	nondimensional parameter
\(\rho\)	density
\(\rho_a\)	ambient air density
\(\rho_0\)	standard atmospheric density (slugs/ft^3 )
\(\sigma\)	air density ratio \((\rho_{\alpha} / \rho_0)\)
\(\sigma_{\mathrm{cr}}\)	critical density
\(\tau\)	shear stress (pounds per square inch) psi
\(\tau_R\)	Roll Mode Time Constant (sec)
\(\phi\)	bank angle (degrees)
\(\psi\)	aircraft heading (degrees)
\(\omega\)	frequency
\(\omega\)	rotational velocity (radians per second)
\(\omega_d\)	damped natural frequency
\(\omega_n\)	natural undamped frequency

1.4 Common Subscripts

Subscript	Meaning
a	aileron
a	ambient
\(\mathrm{alt}\)	at test altitude
\(\mathrm{avg}\)	average
c	calibrated
e	elevator
e	equivalent
E	endurance leg of mission
F	final
I	initial
i	inbound leg of mission
i	indicated
\(\mathrm{ic}\)	instrument corrected
l	subscript for coefficient of rolling moment
m	mission conditions
m	pitching moment
n	yawing moment
O	outbound leg of mission
0	sea-level standard day
0	sea level
r	reserve leg of mission
r	rudder
S	standard day
s	standard day at altitude
\(\mathrm{SL}\)	sea level
T	True
t	test day

1.5 Common Abbreviations

Abbreviation	Meaning
\(a\)	lift curve slope
\(a\)	linear acceleration (ft/sec2 or m/sec2)
\(a\)	speed of sound
A/A	air-to-air
a/c	aircraft
AAA	anti aircraft artillery
AC	aerodynamic center
ac	alternating current
ACM	air combat maneuvering
A/D	analog to digital
ADC	air data computer
ADC	analog-to-digital converter
ADF	automatic direction finder
ADI	attitude direction indicator
AFMC	Air Force Materiel Command
AFOTEC	Air Force Operational Test and Evaluation Center
A/G	air-to-ground
AGL	above ground level
AHRS	attitude heading reference system
AM	amplitude modulation
AOA	angle of attack
AOED	age of ephemeris data
APU	auxiliary power unit
AR	air refuel (mode of flight)
AR	aspect ratio = b2 / S
ARDP	advanced radar data processor
ARSP	advanced radar signal processor
ASPJ	airborne self protection jammer
ATC	air traffic control
avg	average
\(a_x\)	longitudinal acceleration
\(a_y\)	lateral acceleration
AZ	azimuth
\(b\)	span of wing (feet)
B/N	bombardier/navigator
bbl	barrel
BHP	brake horsepower
BICOMS	bistatic coherent measurement system
BID	bus interface device
BIT	built-in test
BSFC	brake specific fuel consumption
Btu	British thermal unit
BW	bandwidth
°C	degrees centigrade (see T)
\(c\)	brake specific fuel consumption (BSFC)
\(c\)	speed of light in a vacuum (186,282 miles/sec = 299,792,500 [m/s])
\(c\)	mean aerodynamic chord (MAC) of a wing
C/A	coarse acquisition
\(C/N_0\)	carrier to noise ratio
CADC	central air data computer
CARD	cost analysis requirement document
\(C_D\)	coefficient of drag
\(C_{D_i}\)	induced drag coefficient
\(C_{D_0}\)	zero lift drag coefficient (also parasitic drag coefficient for symmetric wing)
CDI	course deviation indicator
CDMA	code division multiplex access
CDR	critical design review
CDRL	contracts data requirement list
CDU	control display unit
CEA	circular error average
CEP	circular error probable
\(C_f\)	coefficient of friction
CFE	contractor furnished equipment
CFT	conformal fuel tank
cg	center of gravity (normally in % MAC)
\(C_H\)	hinge moment coefficient
cine	cinetheodolite
\(C_l\)	rolling moment coefficient, airfoil section lift coefficient
\(C_L\)	lift coefficient
CLHQ	closed loop handling qualities
\(C_{\mathrm{lp}}\)	roll damping coefficient
\(C_{\mathrm{lr}}\)	roll moment due to yaw rate coefficient
\(C_m\)	pitching moment coefficient
\(C_M\)	moment coefficient
cm	centimeters
cos	cosine
cot	cotangent
\(C_{l_{\beta}}\)	(dihedral) rolling moment due to sideslip
\(C_{l_{\delta_a}}\)	aileron power coefficient
\(C_{m_q}\)	pitch damping coefficient
\(C{m_{\alpha}}\)	longitudinal static stability coefficient
\(C{m_{\delta e}}\)	elevator power coefficient
\(C_n\)	yawing moment coefficient
\(C_{n_r}\)	yaw damping coefficient
cnst	constant
\(C_{n_{\beta}}\)	directional stability coefficient
\(C_{n_{\delta a}}\)	adverse yaw coefficient
\(C_{n_{\delta r}}\)	rudder power coefficient
COTS	commercial, off–the-shelf
CP	center of pressure
\(C_P\)	propeller power coefficient
CPU	central processing unit
\(c_r\)	wing root chord
CRM	crew resource management
\(c_t\)	wing tip chord
CTF	combined test force
CY	calendar year
\(C_Y\)	side force coefficient
\(C_{Y_{\beta}}\)	side force due to sideslip coefficient
\(C_{Y_{\delta r}}\)	side force due to rudder coefficient
D	diameter
D	drag
D/A	digital/analog
DAC	digital to analog converter
DAPS	data acquisition and processing system
DARPA	Defense Advanced Research Projects Agency
db	decibel
DC	direct current
deg	degrees
DG	directional gyro
DGPS	differential GPS
DMA	Defense Mapping Agency
DME	distance measuring equipment
DoD	Department of Defense
DOP	dilution of precision
DSN	defense switched network
DT	development test
DTC	data transfer cartridge
DTIC	Defense Technical Information Center
\(e\)	Oswald efficiency factor
\(\mathrm{e}\)	natural mathematical constant = 2.718 281 828 459
E	energy
E	lift-to-drag ratio ( \(C_L / C_D\) , \(L/D\) )
EAS	equivalent airspeed
EC	electronic combat
ECCM	electronic counter countermeasures
ECM	electronic countermeasures
ECP	engineering change proposal
ECS	environmental control system
EGT	exhaust gas temperature
EL	elevation
ELINT	electronic intelligence
ELV	expendable launch vehicle
EM	electromagnetic
\(E_{\mathrm{max}}\)	maximum lift-to-drag ratio
EMC	electromagnetic compatibility
EMI	electromagnetic interference
EMP	electromagnetic pulse
EO	electro optical
EOM	equations of motion
EPR	engine pressure ratio
EPROM	electrically programmable read only memory
\(E_s\)	specific energy
ESA	European Space Agency
ESD	Electronic Systems Division
ESHP	equivalent shaft horsepower
ETA	estimate time of arrival
ETE	estimate time en-route
EW	early warning
EW	electronic warfare
°F	degrees Fahrenheit
\(f\)	frequency…hertz (originally cycles per second)
F.S.	fuselage station
\(F_a\)	aileron force
FAA	Federal Aviation Administration
FAR	Federal Aviation Regulation
FCF	functional check flight
FDC	flight data computer
\(F_e\)	elevator force
\(F_{\mathrm{ex}}\)	excess thrust
\(F_g\)	gross thrust
FL	flight level
FLIP	flight information publication
FLIR	forward-looking infrared
FM	frequency modulation
FMC	fully mission capable
FMS	flight management system
FMS	foreign military sales
\(F_n\)	net thrust
\(F_n / \delta\)	corrected thrust parameter
FOM	figure of merit
FOT&E	follow-on test & evaluation
FOUO	for official use only
FOV	field of view
fpm	feet per minute
fps	feet per second
FQT	formal qualification test
\(F_r\)	rudder force
FRD	functional requirements document
FRL	fuselage reference line
FRL	force, rudder, left
FRR	force, rudder, right
FRR	flight readiness review
FSD	full scale development
FSI	full scale integration
ft	feet
ft-lb	English unit of work...foot-pound...
fwd	forward
FY	fiscal year
\(g\)	acceleration due to gravity at altitude
\(G\)	gravitational constant = 6.6732x10-11 [N m2/kg2]
GAO	Government Accounting Office
GCA	ground control approach
GCI	ground controlled intercept
GDOP	geometric dilution of precision
GMT	Greenwich mean time
\(g_0\)	standard acceleration due to gravity (sea level, 46 deg latitude)
GPS	global positioning system
GS	ground speed
GSI	glide slope indicator
\(h\)	% MAC
\(H\)	altitude
HARM	high-speed anti-radiation missile
\(H_c\)	calibrated altitude (assumed to be pressure altitude in flight test)
\(H_D\)	density altitude
HDDR	high density digital recorder
HDOP	horizontal dilution of precision
HF	high frequency
Hg	mercury
\(H_i\)	indicated altitude
\(h_m\)	stick-fixed maneuver point (%MAC)
\(h_{'m}\)	stick-free maneuver point (%MAC)
\(h_n\)	stick-fixed neutral point (%MAC)
\(h_{'n}\)	stick-free neutral point (%MAC)
hp	horsepower
hr	hour
hrs	hours
HSI	horizontal situation indicator
HUD	head-up display
HV	host vehicle
Hz	hertz
I/O	input/output
IAS	indicated airspeed
IAW	in accordance with
ICAO	International Civilian Aviation Organization
ICU	interface computer unit
ICBM	intercontinental ballistic missile
IFF	identification friend or foe
IFR	instrument flight rules
ILS	instrument landing system
IMC	instrument meteorological conditions
IMN	indicated Mach number
IMU	inertial measuring unit
in	inch
INS	inertial navigation system
INU	inertial navigation unit
IOC	initial operational capability
IOT&E	initial operational test & evaluation
IUGG	International Union of Geodesy and Geographics
\(I_x \text{, } I_x\text{, } I_z\)	moments of inertia
\(I_{xy}\text{, }I_{xz}\text{, } I_{yz}\)	products of inertia
J	joules energy, (Newton-Meter)
J	propeller advance ratio
J&S	jamming and spoofing
JCS	Joint Chiefs of Staff
K	Kelvin (absolute temperature)
K	temperature probe recovery factor
\(K\text{, }k\)	constants
KCAS	knots calibrated airspeed
KEAS	knots equivalent airspeed
kg	kilogram, metric unit of mass
KIAS	knots indicated airspeed
KISS	keep it simple, stupid
km	kilometer
KTAS	knots true airspeed
kt	knots
\(L\)	Lift (lbs)
\(l\)	length
\(L\)	rolling moment
L/D	Lift-to-drag ratio
LANTIRN	low altitude navigation and targeting IR for night
lat	lateral
lb	pound
lbf	English unit of force, often just lb (pound)
lbm	English unit of mass, often just lb (slug)
LCC	life cycle cost
LCD	liquid crystal display
LED	light emitting diode
LLH	latitude, longitude, height
\(\ln\)	natural log, log to the base \(\mathrm{e}\)
LO	low observables
Log	common log, to the base 10
LOS	line of sight
\(l_t\)	distance from \(cg\) to tail’s aerodynamic cent
\(L_{\delta a}\)	rolling moment due to aileron deflection
\(M\)	moment (ft-lbs)
\(M\)	Mach number
\(m\)	mass
m	meter (length)
\(M\)	pitching moment
MAG	magnetic
MAP	manifold pressure
mb	millibar
MCA	minimum crossing altitude
\(M_{\mathrm{cr}}\)	critical Mach number
\(M_d\)	drag divergence Mach number
\(M_{\mathrm{ac}}\)	mean aerodynamic cord
\(M_{\mathrm{GC}}\)	mean geometric chord
MHz	megahertz
mHZ	millihertz
\(M_{\mathrm{ic}}\)	instrument-corrected Mach number
MilSpec	military specification
MIL-STD	military standard (publication)
min	minute (time)
mm	millimeter
MOA	memorandum of agreement
MOE	measure of effectiveness
MOP	measures of performance
MOU	memorandum of understanding
MP	manifold pressure
MSL	mean sea level
MTBF	mean time between failures
MTTR	mean time to repair
MX	maintenance
N	newton (force)
\(N\)	rotational speed (RPM)
\(n\)	load factor (g's)
\(N\)	yawing moment
\(N_1\)	low pressure compressor speed
\(N_2\)	high pressure compressor speed
NACA	National Advisory Committee for Aeronautics
NADC	Naval Air Development Center
NASA	National Aeronautics and Space Administration
NAV	navigation
NED	North, East, Down
NM, nm	nautical mile (6080 feet)
NOE	nap-of-the-earth
NOFORN	not releasable to foreign nationals
NOTAM	notice to airmen
NRC	National Research Council (Canada)
NWC	Naval Weapons Center
\(N_x\)	longitudinal load factor (g's)
\(N_y\)	lateral load factor (g's)
\(N_z\)	normal load factor (g's)
OAT	outside air temperature
OAT	on aircraft test
OEI	One engine inoperative
OPR	Office of Primary Responsibility
OSD	Office of the Secretary of Defense
OT&E	operational test & evaluation
\(p\)	aircraft roll rate (degrees/sec)
\(P\)	pressure (N/m2 ,pounds per square inch)
\(P_a\)	ambient pressure
PCM	pulse code modulation
P-code	precision code
PD	pulse Doppler
PDM	pulse duration modulation
PGM	precision guided munitions
PIO	pilot induced oscillations
\(P_{\mathrm{iw}}\)	total thrust horsepower required
Pk	probability of kill
PLF	power for level flight
\(P_0\)	standard atmospheric pressure (2116.22 lb/ft2 )
POC	point of contact
\(P_p\)	pitot pressure
ppm	parts per million
Prop	propeller
\(P_s\)	specific power
\(P_s\)	static pressure
PS	pulse search
psf	pounds per square foot
psi	pounds per square inch
\(P_T\)	total pressure
PW	pulse width
\(Q\) or \(q\)	dynamic pressure = \(0.5 \rho V^2\)
q	aircraft pitch rate
Q	engine torque
\(q_c\)	impact pressure (\(P_t − P_a\))
°R	degrees Rankine = °F + \(459.67\)
R	perfect gas constant = \(8314.34 \left[ \text{J/kmol K} \right]\)
r	aircraft yaw rate (degrees/sec)
R	earth radius
R	range
R&D	research and development
R&M	reliability and maintainability
R/C	rate of climb
rad	radians
Radar	radio detection and ranging
RAF	resultant aerodynamic force
RAM	radar absorbing material
RAT	ram air turbine
RCS	radar cross section
Re	Reynolds number (dimensionless)
REP	range error probable
RF	range factor
RLG	ring laser gyro
rms	root mean square
RNG	range
ROC	rate of climb
ROC	required obstacle clearance
RPM	revolutions per minute (a.k.a. N)
R/T	receiver/transmitter
RTO	Rejected/refused takeoff
RTO	responsible test organization
\(S\)	wing area (ft2 or m2)
\(S_a\)	horizontal distance between liftoff and specified height or between specified height and touch down
SA	selective availability
SA	situational awareness
SE	specific endurance
sec	seconds (time or angle)
SFC	specific fuel consumption
\(S_g\)	ground roll distance
SHP	shaft horsepower
SI	international system of units
SIGINT	signal intelligence
sin	sine
SL	sea level
SLAM	standoff land attack missile
SLR	side-looking radar
S/N	serial number
S/N	signal -to-noise ratio
SOF	special operations forces
SOW	stand-off weapon
SR	specific range
SRB	safety review board
\(S_T\)	tail area
std	standard
\(S_T\)	total takeoff or landing distance \(S_a + S_g\))
STOL	short takeoff and landing
STOVL	short takeoff and vertical landing
\(T\)	period of oscillation
\(T\)	temperature
\(t\)	thickness
\(T\text{, }t\)	time (sec)
t/c	thickness-to-chord ratio
\(T_a\)	ambient temperature
TACAN	tactical air navigation
tan	tangent
\(T_{\mathrm{as}}\)	standard temperature at altitude
TAS	true airspeed
TBD	to be determined
TD	touchdown
TED	trailing edge down
TEL	trailing edge left
TEMP	test and evaluation master plan
TER	trailing edge right
TEU	trailing edge up
TF	terrain following
\({\mathrm{THP}}\)	Thrust Horsepower
\({\mathrm{THP}}_{\mathrm{alt}}\)	horsepower available at altitude
\({\mathrm{THP}}_{\mathrm{max}}\)	maximum horsepower available
\({\mathrm{THP}}_{\mathrm{min}}\)	minimum horsepower required
\({\mathrm{THP}}_{\mathrm{SL}}\)	horsepower required at sea level
TIT	turbine inlet temperature
TM	telemetry
TMN	true Mach number
T/O	takeoff
\(T_0\)	standard sea level temperature ( \(59.0°\)F, \(15°\)C)
TO	technical order
TRB	technical review board
TRD	technical requirements document
TRP	technical resources plan
TSFC	thrust specific fuel consumption
TSPI	time, space, position information
\(T_t\)	total temperature
TV	television
T/W	thrust to weight ratio
TWT	track while scan
TWT	traveling wave tube
\(u\)	velocity along aircraft's x-axis
UAV	uninhabited aerial vehicle
UHF	ultra high frequency
UPT	undergraduate pilot training
USA	US Army
USAF	US Air Force
USCG	US Coast Guard
USMC	US Marine Corps
USN	US Navy
UT	universal time
UV	ultraviolet
\(v\)	velocity along aircraft's lateral axis
\(V_H\)	horizontal tail volume coefficient
\(V_V\)	vertical tail volume coefficient
\(V_1\)	takeoff decision speed
\(V_2\)	takeoff safety speed
\(V_A\)	design maneuvering speed
VAC	volts AC
\(V_b\)	buffet airspeed
\(V_B\)	design speed for max gust intensity
\(V_{\mathrm{br}}\)	velocity for best range
\(V_c\)	calibrated airspeed
\(V_D\)	design diving speed
VDC	volts DC
VDOP	vertical dilution of precision
\(V_e\)	equivalent velocity
\(V_{\mathrm{FE}}\)	maximum flap extended speed
VFR	visual flight rules
\(V_g\)	ground speed
VHF	very high frequency
\(V_i\)	indicated airspeed
\(V_{\mathrm{ic}}\)	indicated airspeed corrected for instrument error
\(V_{\mathrm{iw}}\)	velocity at sea level std day and std weight
VLE	max speed with landing gear extended
\(V_{\mathrm{LO}}\)	max speed while operating landing gear
\(V_{\mathrm{LOF}}\)	lift off speed
VLSIC	very large scale integrated circuit
\(V_{\mathrm{mc}}\)	minimum directional control speed
VMC	visual meteorological conditions
\(V_{\mathrm{mca}}\)	minimum directional control speed in the air
\(V_{\mathrm{mcg}}\)	minimum directional control speed on the ground
\(V_mo/M_mo\)	maximum operating limit speed
\(V_{\mathrm{mu}}\)	minimum unstick speed
\(V_{\mathrm{NE}}\)	never exceed velocity
\(V_{\mathrm{no}}\)	max structural cruising speed
\(V_{\mathrm{opt}}\)	optimum velocity for endurance flight
VOR	VHF omni-directional range
VORTAC	VOR + TACAN
\(V_{P_{\mathrm{min}}}\)	velocity for minimum power
\(V_{P_{\mathrm{min}_{\mathrm{SL}}}}\)	velocity for minimum power at sea level
\(V_R\)	rotation speed
\(V_S\)	stall speed
\(V_{S_0}\)	stall speed in landing configuration
\(V_{S_1}\)	stall speed in some defined configuration
VSTOL	vertical/short takeoff and landing
\(V_T\)	true airspeed
VTOL	vertical takeoff & landing
VVI	vertical velocity indicator
\(V_W\)	wind velocity
\(V_X\)	speed for best angle of climb
\(V_Y\)	speed for best rate of climb
\(W\)	weight
\(w\)	component of velocity along aircraft's Z-axis
WDL	weapon data link
\(W / \delta\)	weight-to-pressure ratio
\(W_f\)	fuel weight
WGS-84	World Geodetic System, 1984
WI	watch item
WIT	watch item
WOD	word of day
WOW	weight on wheels
WPT	waypoint
wrt	with respect to
\(\frac{\dot{W_f}}{\delta \sqrt{\theta}}\)	corrected fuel flow parameter
W/S	wing loading
\(W_f\)	fuel flow (lb/hr)
\(x\)	aircraft longitudinal axis, a line running through the nose & tail
\(X_{\mathrm{ac}}\)	distance from leading edge to aerodynamic center
Xlink	cross link
\(y\)	aircraft lateral axis, a line running the wingtips
\(Y\)	force along y-axis
Y-code	encrypted P-code
\(z\)	aircraft vertical or yaw axis, a line perpendicular to the longitudinal and lateral axes
\(\Delta H_{\mathrm{ic}}\)	altimeter instrument correction
\(\Delta H_{\mathrm{pc}}\)	altimeter position error correction
\(\Delta P_{p}\)	pitot pressure error
\(\Delta P_{s}\)	static pressure error
\(\Delta V_{c}\)	scale attitude correction to airspeed
\(\Delta V_{\mathrm{ic}}\)	instrument correction to airspeed indicator
\(\Delta V_{\mathrm{pc}}\)	correction for airspeed position error
\(\infty\)	infinity, or freestream conditions

1.6 Sign Conventions

(Roberts 1997)

Editor’s note There is near unanimous agreement on most sign conventions except for pilot inputs and control surface deflections. Although individual organizations generally are consistent in-house, confusion often arises when trying to mathematically translate inputs & deflections from one organization to another. This section documents the generally accepted “body axes” sign conventions then discusses the rationale for several viewpoints addressing the “inputs & deflections” debate. Below is the SFTE sign convention.

Wind Axes Sign Convention

Winds are listed according to the direction they are coming from. Airports refer winds to magnetic North while winds at altitude are typically referred to true North. Headwind is true airspeed minus ground speed. (\(V_w =V_T - V_g\)).

Body Axes Sign Convention

The generally accepted body axes sign convention is based on the establishment of a three-dimensional axis system with the following properties:

1. It is right-handed orthogonal

2. Its origin is at the vehicle's reference center of gravity (defined by builder).

3. The axis system moves with the airframe.

Translational displacements, rates, accelerations, & forces are positive along the positive body axes directions. In spite of the simplicity of this logic, it is important to recognize that lift and normal load factor are positive in the negative z direction and the drag is positive in the negative x direction.

Angular displacements, rates, accelerations & moments, are positive according to the “right hand rule” (a clockwise rotation while looking in the direction of the positive axis) as shown in the figure.

The body axes, forces & translations along them, and moments & rotations about them are shown with arrows indicating the positive direction.

Angular displacements, rates, accelerations & moments, are positive according to the “right hand rule” (a clockwise rotation while looking in the direction of the positive axis) as shown in the figure.

The body axes, forces & translations along them, and moments & rotations about them are shown with arrows indicating the positive direction.

Angle of attack is positive clockwise from the projection of the velocity vector on the xz plane to the reference x body axis. The angle of sideslip is positive clockwise from the xz plane to the velocity vector (wind in the pilot’s right ear).

Aircraft true heading is the angle between true North and the projection of the x-body axis onto the horizontal plane. Mag. heading refers to mag North

The velocity vector is measured relative to the air mass while the flightpath is measured relative to the ground. They are equivalent only when winds are zero.

Flightpath heading angle (ground track heading) \(\sigma_g\), is the horizontal angle between true North and the projection of the flightpath on the horizontal plane. Positive rotation is from north to east.

Flightpath elevation angle; γ, is the vertical angle between the flightpath and the horizontal plane. Positive rotation is up. During a descent, this parameter is commonly known as glide path angle.

Flightpath bank angle; \(\mu\), is the angle between the plane formed by the velocity vector and the lift vector and the vertical plane containing the velocity vector. Positive rotation is clockwise about the velocity vector, looking forward.

Fuselage reference station (FRS), Water line (WL), and Buttock line (BL) are reference coordinates established by the design group.

Summary of Generally Accepted Body Axes Sign Convention
Parameter Name	Symbol	Positive Direction
Translational Measurements
Longitudinal axis	\(x\)	from ref cg towards nose
Lateral axis	\(y\)	from reference cg towards right wing tip
Vertical axis	\(z\)	from reference cg towards vehicle bottom (body axis)
Longitudinal velocity	\(u\)	along +x axis
Lateral velocity	\(v\)	along +y axis
Vertical velocity	\(w\)	along +z axis
Longitudinal acceleration	\(a_x\)	along +x axis
Lateral acceleration	\(a_y\)	along +y axis
Vertical acceleration	\(a_z\)	along +z axis
Longitudinal load factor	\(N_x\)	along +x axis
Lateral load factor	\(N_y\)	along +y-axis
Normal load factor	\(N_z\)	along -z axis
Longitudinal force	\(F_x\)	along the +x axis
Lateral force	\(F_y\)	along the +y axis
Normal force	\(F_z\)	along the + z axis
Drag force	\(D\)	along the -x axis
Side force	\(Y\)	along the + y axis
Lift Force	\(L\)	along the -z axis

Summary of Generally Accepted Body Axes Sign Convention

Parameter Name	Symbol	Positive Direction
Angular Measurements
Bank angle	\(\phi\)	right wing down
Pitch angle	\(\theta\)	nose-up
Heading	\(\psi\)	0 North, +Eastward
Angle of attack	\(\alpha\)	normal flight attitude
Angle of sideslip	\(\beta\)	“wind in the right ear”
Roll rate	\(p\)	right wing down
Pitch rate	\(q\)	nose up
Yaw rate	\(r\)	nose right
Roll moment	\(L\)	right wing down
Pitch moment	\(M\)	nose up
Yaw moment	\(N\)	nose right
Flightpath bank angle	\(\mu\)	right wing down
Flightpath elevation	\(\gamma\)	climb
Flightpath heading	\(\sigma_g\)	0 true North, + East- ward

Discussion of “Input & Deflection” Conventions

The debate regarding proper inputs and deflections stems from the user’s viewpoint. From the body axis convention above, flight testers recognize that a climbing right turn generates positive angular measurements. Logically then, pull, right roll and right yaw pilot inputs and subsequent surface deflections should also be positive. The traditional flight tester’s convention follows as “All input forces & displacements, surface deflections, and motions that cause a climbing right turn are positive.”

Due to differential nature of aileron deflections, they require more discussion. The flight tester’s logic implies (but does not dictate) positive deflections are right aileron up and left aileron down. It is, however, equally acceptable to assign downward (or upward) deflection as positive for both ailerons and calculate the difference between the two as a measure of rolling moment.

The rationale within the wind tunnel community is also logical: any control surface deflection that increases lift is positive. From this, positive deflections are trailing edge down (TED) for each: trailing edge flap, stabilizer, elevator, stabilator, rollervator, ruddervator, canard, aileron, flaperon, and all their tabs. Leading edge flap down is also positive. Similarly, since side force is positive to the right, then positive rudder and rudder tab deflections are trailing left (TEL). The only exception to this straightforward logic is for spoilers and speed brakes that extend only in one direction: this deflection is positive even though it might decrease the lift.

Since the above rationale defines downward deflection as positive for both ailerons, a measurement of rolling moments requires calculation of the differential aileron deflection. This rationale does not, however, specifically dictate whether a “positive” differential deflection should generate right wing down (RWD) or left wing down (LWD) moments. Differential aileron can be calculated as either.

\(\delta_{a} = \frac{\delta_{\mathrm{a_R}} - \delta_{\mathrm{a_L}}}{2}\) or \(\delta_{a} = \frac{\delta_{\mathrm{a_L}} - \delta_{\mathrm{a_R}}}{2}\)

Selection of the RWD convention is obvious from the flight tester’s viewpoint since deflections that generate right rolls are positive. An alternative interpretation is that a positive differential aileron deflection is one that lifts the positive (right) wing lifts more than the left (LWD).

Another common convention for ailerons is one that gives the same sign to both ailerons for any input. The “right hand screw” convention is opposite to the flight tester’s convention, but may be more common:

\(\delta_{a_R} = +\mathrm{TED}\), \(\delta_{a_L} = +\mathrm{TEU}\).

The above wind tunnel rationale dictates only the polarity for individual control surface deflections, and leaves open the sign convention debate about controller (inceptor) input forces & displacements. One approach is that positive inputs should generate positive motions while an alternate approach is that positive inputs generate positive surface deflections. Only the flight tester’s convention states that positive inputs yield positive motions and deflections. All approaches are mathematically connected to the hinge moment sign convention discussed below.

The simplest control surface hinge moment convention is that all positive hinge moments (generated by the pilot and the aerodynamics) move the surface in a positive direction, i.e., positive input forces yield positive deflections. This has different implications for the different sign conventions:

• According to the above flight tester’s sign convention, a positive pull force is required to generate a positive (TEU) elevator deflection (positive stick force generates a climb).

• According to wind tunnel sign convention, a positive push force is required to generate a positive (TED) elevator deflection (positive stick force generates a dive).

The alternate viewpoint defines a positive inceptor hinge moment as one that opposes the aerodynamic moments. In other words, a positive inceptor hinge moment moves the surface to a position which generates positive aerodynamic hinge moments or “positive input forces & displacements generate negative surface deflections.”

Based on the above background, the SFTE technical council proposes the following standard convention for inceptor & surface forces & deflections:

• Due to its widespread use and its simple & robust nature, use the wind tunnel convention for control surface deflections.

• Due to widespread test pilot & FTE familiarity and logical nature, use the flight tester’s convention that positive inceptor forces & displacements generate a climbing right turn.

• A fallout from these conventions is that positive inceptor hinge moments generate positive aerodynamic hinge moments (negative surface deflections).

• Consistent use of the above logic requires that the calculated value for aileron deflection be negative for right wing down moments. Similarly, differential ruddervator deflections generating nose right yawing moments should have negative values.

 

Conventions for Positive Control Surface Deflections

Parameter	Symbol	Flight Test	SFTE/ Wind Tunnel
Horizontal Stabilizer	\(\delta_i\)	TEU	TED
Elevator	\(\delta_e\)	TEU	TED
Elev. Tab	\(\delta_{et}\)	TED	TED
Stabilators or Rollervators,	\(\delta_{eL}\), \(\delta_{eR}\)	TEU	TED
average:	\(\delta_e\)	\(\frac{\delta_{eR} + \delta_{eL}}{2}\)
differential:	\(\Delta\delta_e\)	\(\frac{\delta_{eR} - \delta_{eL}}{2}\)
Elevons	\(\delta_{vL}\), \(\delta_{vR}\)	TEU	TED
average:	\(\delta_v\)	\(\frac{\delta_{vR} + \delta_{vL}}{2}\)
differential:	\(\Delta\delta_v\)	\(\frac{\delta_{vR} - \delta_{vL}}{2}\)
Flaperons or trailing edge flap	\(\delta_{fL}\), \(\delta_{fR}\)	TED	TED
average:	\(\delta_f\)	\(\frac{\delta_{fR} + \delta_{fL}}{2}\)
differential:	\(\Delta\delta_f\)	\(-\frac{\delta_{fR} - \delta_{fL}}{2}\)	\(\frac{\delta_{fR} - \delta_{fL}}{2}\)
Canards	\(\delta_{cL}\), \(\delta_{cR}\)	TED	TED
average:	\(\delta_c\)	\(\frac{\delta_{cR} + \delta_{cL}}{2}\)
differential:	\(\Delta\delta_c\)	\(-\frac{\delta_{cR} - \delta_{cL}}{2}\)	\(\frac{\delta_{cR} - \delta_{cL}}{2}\)
Leading edge flap	\(\delta_{lefL}\), \(\delta_{lefR}\)	Leading Edge Down	Leading Edge Down
Ruddervators	\(\delta_{rvL}\), \(\delta_{rvR}\)	TEU	TED
average:	\(\delta_{rv}\)	\(\frac{\delta_{rvR}+\delta_{rvL}}{2}\)
differential:	\(\Delta\delta_{rv}\)	\(-\frac{\delta_{rvR} - \delta_{rvL}}{2}\)
Ailerons	\(\delta_{aL}\), \(\delta_{aR}\)	\(\delta_{aR}\) TEU & \(\delta_{aL}\) TED or \(\delta_{aR}\) & \(\delta_{aL}\) TED	\(\delta_{aR}\) & \(\delta_{aL}\) TED
Aileron Tab	\(\delta_{at}\)	\(\frac{\delta_{aR}+\delta_{aL}}{2}\)	\(\delta_{at}\) TED
average:	\(\delta_{a}\)	\(-\frac{\delta_{aR} - \delta_{aL}}{2}\)	\(\frac{\delta_{aR} - \delta_{aL}}{2}\)
Spoilers	\(\delta_{sL}\), \(\delta_{sR}\)	Extended	Extended
average:	\(\delta_{s}\)	\(\frac{\delta_{sR}+\delta_{sL}}{2}\)
differential:	\(\Delta\delta_{s}\)	\(\frac{\delta_{sR} - \delta_{sL}}{2}\)	\(-\frac{\delta_{sR} - \delta_{sL}}{2}\)
Rudders	\(\delta_{rL}\), \(\delta_{rR}\)	TER	TEL
average:	\(\delta_{r}\)	\(\frac{\delta_{rR}+\delta_{rL}}{2}\)
Rudder tab	\(\delta_{rt}\)	TEL
Speed brake	\(\delta_{sb}\)	Extended

Conventions for Positive Inputs and Hinge Moments

Parameter	Symbol	Flight Test	SFTE/ Wind Tunnel
Stick/Wheel Long Force	\(F_e\)	Pull
Stick/Wheel Lateral Force	\(F_a\)	Right
Pedal Force	\(F_r\)	Right pedal push
Stick/Wheel Longitudinal deflection	\(\delta_{s_e}\)	Aft
Stick/wheel Lateral deflection	\(\delta_{s_a}\)	Right
Pedal deflection	\(\delta_{pR}\), \(\delta_{pL}\)	Right pedal push
Aerodynamic Hinge Moments	\(C_{h_\delta}\) \(C_{h_\alpha}\) \(C_{h_{\delta_o}}\) \(C_{h_{\delta_\text{tab}}}\)	positive moments generate positive deflections
Inceptor Hinge Moments	\(C_{h_{F_e}}\) \(C_{h_{F_a}}\) \(C_{h_{F_r}}\)	+ moments generate + deflections	+ moments generate - deflections

*The wind tunnel rationale does not inherently define the polarity for control surface differential deflections.

#The wind tunnel rationale does not specify a convention for positive inputs or hinge moments. Historically, Dutch, U.S. and some British aircraft use a climbing right turn, while it is a diving left turn for Canadian, Australian, and some British aircraft.

The SFTE Technical Council recognizes that several combinations of the above possibilities are currently in use around the world, and invites comments, additions, or corrections to the above summary and proposal. Although SFTE does not expect all organizations to adopt this standard, it still provides a cornerstone for reference purposes

1.7 Thermodynamics Relations

(Jones and Hawkings 1960; Eshbach 1936; Potter and Somerton 1993; Abbott and Van Ness 1989)

1.7.1 Thermodynamic Definitions

A Process is an event with a redistribution of energy within a system.

A Reversible process is one that can be reversed such that the system returns to its original state (form, location & amount).

An Irreversible process cannot return to its original state due to heat flow from higher to lower temperatures, fluid turbulence, friction, or inelastic deformation. The change in entropy is non-zero.

An Isothermal process is one in which the temperature of the fluid is constant.

An Adiabatic process is one in which heat is not transferred to or from the fluid.

Work is the energy transfer by way of changing mechanical energy.

Heat is the energy transfer from one body to another by virtue of a temperature difference between them.

An Isentropic process has constant entropy.

Conduction is the energy transfer from a warmer body by tangible contact (transfer of some internal molecular kinetic energy).

Convection is the repositioning the energy of a fluid without state changes or energy transformations (e.g. heated air moving from one room to another room).

Radiation is the energy transmission through space.

1.7.2 Thermodynamic Symbols

Symbol	Use
\(A\)	area
\(C\)	compressibility factor
\(c\)	speed of sound
\(E = u\)	specific internal energy (e.g. Btu/lb)
\(H\)	specific enthalpy (e.g. Btu/lb)
\(J\)	Joule
\(Q\)	energy supplied to a system or region as heat (e.g. Btu/lb)
\(P\)	absolute pressure (e.g. lbs/ft2)
\(V\)	specific volume (e.g. ft3/lb)
\(W\)	work (+ if entering)
\(\overline{V}\)	velocity
\(\Delta\)	change ( final - initial value)
\(Z\)	altitude
\(S\)	specific entropy
\(R\)	gas constant for each gas (for air = 287 J/kg/K = 53.35 ft-lb/lbmR)
\(\overline{R}\)	universal gas constant = 8.314 kJ/kmol/K = 1545 ft lb/lbmol/R
\(M\)	molar mass (for air = 28.97 kg/kmol)
\(N\)	number of moles
\(\rho\)	density

1.7.3 Thermodynamic Laws

The First Law of Thermodynamics shows that the net amount of energy added to a system equals the net change in energy within the system (Principle of Conservation of Energy): \(W + Q = (E_2 - E_1)\)

The Second Law of Thermodynamics states that entropy increases during any irreversible process: \(S_2 > S_1\)

Ideal Gas Equation of State (a.k.a. Perfect gas law):

\[ \begin{align} PV&=RT\\ P &= \rho RT\\ PV &= mRT\\ PV &= nRT\\ \end{align} \]

\(\delta = \sigma \theta\)

where

\[ \begin{align} \delta &= \frac{P_a}{P_0}\\ \sigma &= \frac{\rho_a}{\rho_0}\\ \theta &= \frac{T_a}{T_0} \end{align} \]

Boyle’s Law states that when the temperature of a given mass of gas is held constant, then the volume and pressure vary inversely.

\(P_1 V_1 = P_2 V_2\)

where \(T_1 = T_2\)

Charles’ Law states that when a volume of a given mass is held constant, then the change in pressure of the gas is proportional to the change in temperature.

\(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)

where \(V_1 = V_2\)

Real Gas Relation:

\(PV = CRT\)

For reversible processes:

\[ \begin{align} W &= −\int_{}^{}{PdV}\\ Q &= \int_{}^{}{TdS} \end{align} \]

For reversible adiabatic processes:

\[ \begin{align} \frac{P_1}{P_2} &= \Bigg[ \frac{V_2}{V_1} \Bigg]^{\gamma} \\ \frac{T_1}{T_2} &= \Bigg[ \frac{V_2}{V_1} \Bigg]^{\gamma - 1} \\ \frac{T_1}{T_2} &= \Bigg[ \frac{P_1}{P_2} \Bigg]^{\frac{\gamma - 1}{\gamma}} \\ \frac{P_1}{P_2} &= \Bigg[ \frac{\rho_1}{\rho_2} \Bigg]^{\gamma} \\ \end{align} \]

Steady Flow Energy Equation

\(Q + H_1 + \frac{\overline{V}_1^2}{2g} + Z_1 = W + H_2 + \frac{\overline{V}_2^2}{2g} + Z_2\)  

Bernoulli Equation:

\(\frac{\Delta P}{\rho g} + \frac{\overline{V}_2^2 - \overline{V}_1^2}{2g} + \Delta Z = 0\)

Flow per Unit Area:

\(\frac{W}{A} = \sqrt{\frac{\gamma}{R} \frac{P}{\sqrt{T}} \frac{M}{\Big( 1 + \frac{\gamma - 1}{2} M^2 \Big) \frac{\gamma + 1}{2 (\gamma - 1)}}}\)

Velocity of sound in a perfect gas:

\(c = \sqrt{\gamma g R T}\)

Development of Specific Heat Relations:

Specific heat at constant pressure (for air = 1004.76 J/kg/K)

\(c_p \equiv \frac{\partial H}{\partial T} \Bigg \rvert_{P}\)

Specific heat at constant volume (for air = 717.986 J/kg/K)

\(c_v \equiv \frac{\partial u}{\partial T} \Bigg \rvert_{V}\)

Ratio of specific heats

\(\kappa = \gamma \equiv \frac{c_p}{c_v}\)

Enthalpy equation in differential form is: \(dH = du + d(PV)\)

Substituting definitions and ideal gas law gives

\[ \begin{align} c_p \, dT &= c_v \, dT + R \, dt\\ &\;\;\mathrm{or} \\ c_p &= c_v + R \end{align} \]

Rearranging gives

\[ \begin{align} c_p &= R \frac{\kappa}{\kappa - 1}\\ &\;\;\mathrm{and} \\ c_v &= R \frac{1}{\kappa - 1} \end{align} \]

Development of Poisson’s Equation:

1) From the 1st law: \(W+Q = E_2-E_1\)

2) Substitution for each term gives: \(T\,dS - P\,dV = du\)

3) Divide through by T: \(dS = \frac{du}{T} + \frac{P\,dV}{T}\)

4) Recall: \(du = c_v\,dT\) and \(PV = RT\)

5) Substitution gives: \(dS = c_v\frac{dT}{T} + R \frac{dV}{V}\)

6) Assume constant specific heat and integrate: \(s_2 - s_1 = c_v\,\ln \frac{T_2}{T_1} + R\,\ln \frac{V_2}{V_1}\)

7) Assuming a reversible adiabatic process: \(c_v\,\ln \frac{T_2}{T_1} = - R\,\ln \frac{V_2}{V_1}\)

8) Substitute \(c_v = R\frac{1}{\kappa - 1}\) to get: \(\frac{T_2}{T_1} = \Big( \frac{V_1}{V_2} \Big)^{\kappa -1}\)

9) Differentiate H: \(dH = du + P\,dV + V\,dP\)

10) Substitution into step #2: \(T\,dS = dH - V\,dP\)

11) Integrate: \(s_2 - s_1 = c_p\,\ln \frac{T_2}{T_1} + R\,\ln \frac{P_2}{P_1}\)

12) Assuming a reversible adiabatic process: \(c_p\,\ln \frac{T_2}{T_1} = - R\,\ln \frac{P_2}{P_1}\)

13) Substitute \(c_v = R\frac{\kappa}{\kappa - 1}\) to get: \(\frac{T_2}{T_1} = \Big( \frac{P_2}{P_1} \Big)^{\frac{\kappa -1}{\kappa}}\)

14) Combine steps #8, #13 to get: \(\frac{P_2}{P_1}=\Big( \frac{V_1}{V_2} \Big)^{\kappa}\) or \((PV)^{\kappa} = \mathrm{const}\)

1.8 Mechanics Relations

1.8.1 Mechanics Symbols

Symbol	Use
\(a\)	linear acceleration
\(a_r\)	centripetal (radial) acceleration
\(a_T\)	tangential acceleration
\(F\)	force
\(g\)	acceleration due to gravity
\(G\)	moment
\(H\)	angular momentum
\(H\)	height
\(Hp\)	horsepower
\(I\)	rotational moment of inertia (see section 10)
\(J\)	impulse = change in momentum
\(k\)	radius of gyration
\(m\)	mass
\(N_r\)	radial load factor
\(P\)	power
\(L\)	linear momentum
\(Q\)	moment (a.k.a. torque)
\(r\)	radius
\(S\)	distance, displacement
\(s\)	seconds
\(t\)	time
\(V\)	true inertial velocity
\(V_0\)	initial inertial velocity
\(W\)	work
\(q\)	angular displacement
\(\mathrm{Vol}\)	volume
\(\omega\)	angular velocity (radians/second)
\(\dot{\omega}\)	angular acceleration

1.8.2 Newton’s Laws

1^st law (law of inertia):

“Every body persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.”

2^nd Law:

“The change in motion is proportional to the motive force impressed and is made in the direction of the straight line in which that force is impressed” (motion defined as velocity x quantity of matter or linear momentum, \(m\,V\) ).

\(dF = \frac{d(mV)}{dt}\)

For constant mass in rectilinear motion: \(F = ma\)

For constant mass distribution in curvilinear motion: \(G = \dot{\omega} I\)

3^rd Law:

“Every action has an equal and opposite reaction; or, the mutual attraction of two bodies upon each other are always equal and directed to contrary parts.(opposite directions)”

1.8.3 Planar Kinetics, Work, Power and Energy

Rectilinear motion		Curvilinear motion
displacement	\(S\)	angular displacement	\(\theta\)
velocity	\(V = \frac{dS}{dt}\)	angular velocity	\(\omega = \frac{d\theta}{dt}\)
acceleration	\(a = \frac{dV}{dt}\)	angular acceleration	\(\dot{\omega} = \frac{d\omega}{dt}\)
inertia	\(m\)	rotational inertia	\(I = \int_{}^{}{r^2 dm}\)
momentum	\(L = m\,V\)	angular momentum	\(H = I \omega\)
force	\(F = m\,a\)	torque	\(Q = I \dot{\omega}\)
work	\(W = \int_{}^{}{F\,dS}\)	work	\(W = \int_{}^{}{Qd\theta}\)
power	\(P = F\,V\)	power	\(P = Q \omega\)
kinetic energy	\(\frac{1}{2} mV^2\)	kinetic energy	\(\frac{1}{2} I \omega^2\)
potential energy	\(mgH\)	n/a

1.8.4 Planar Kinematics at Constant Acceleration

Rectilinear motion	Curvilinear motion
\(V = V_0 + at\)	\(\omega = \omega_0 + \dot{\omega} t\)
\(V^2 = V_0^2 + 2aS\)	\(\omega^2 = \omega_0^2 + 2 \dot{\omega}\theta\)
\(S = V_0 t + \frac{1}{2} a t^2\)	\(\theta = \omega_0 t + \frac{1}{2} \dot{\omega} t^2\)
\(S = \frac{1}{2}(V + V_0) t\)	\(\theta = \frac{1}{2}(\omega + \omega_0)t\)
\(S = \frac{\left( V^{2} - V_{0}^{2} \right)}{2a}\)	\(\theta = \frac{\left( \omega^{2} - \omega_{0}^{2} \right)}{2\dot{\omega}}\)
\(t = \frac{- V_{0} + \sqrt{V_{0}^{2} + 2\text{aS}}}{a}\)	\(t = \frac{- \omega_{0} + \sqrt{\omega_{0}^{2} - 2\dot{\omega}\theta}}{\dot{\omega}}\)
\(a = \frac{2\left( S - V_{0}t \right)}{t^{2}}\)	\(\dot{\omega} = \frac{2(\theta - \omega_{0}t)}{t^{2}}\)

1.8.5 Curvilinear motion with constant acceleration and radius

\(r = \frac{V^2}{g N_r}\)

\(V = \omega r\)

\(N_r = \frac{a_r}{g}\)

\(\omega = \frac{g N_r}{V}\)

\(\dot{\omega} = \frac{\dot{V}}{R}\)

\(a_r = r \omega^2 = \frac{V^2}{r}\)

\(a_{r} = \dot{\omega}r\)

1.8.6 Aircraft in level turn

\(N_{z_w}\) = load factor normal to flight path

\(r\) = turn radius

\(\Omega\) = turn rate (rad/sec)

\(r = \frac{V^{2}}{g\sqrt{N_{\mathrm{zw}}^{2} - 1}}\)

\(\omega = \frac{g\sqrt{N_{\mathrm{zw}}^{2} - 1}}{V}\)

\(N_{z_w} = \sqrt{\frac{\omega V}{g} + 1}\)

\(V\) = inertial velocity

1.8.7 Level Turn Kinematics Character

 

1.8.8 Gyroscopic Motion

(reference 1.7)

For bodies spinning about an axisymmetric axis

\(\dot{\psi}\) = spin rate

\(\dot{\phi}\) = precession rate

\(\dot{\theta}\) = nutation rate

\(I_z\) = moment of inertia about spin axis

\(I_t\) = transverse moment of inertia about the spin point (perpendicular to spin axis)

\(I_{\mathrm{cg}}\) = moment of inertia about the \(\mathrm{cg}\) (perpendicular to spin axis)

\(M_x\) = moment about spin point (acting along plane that defines \(\theta\) )

For steady precession (constant \(\dot{\theta}\), \(\dot{\phi}\) , \(\dot{\psi}\) )

\(\sum M_{x} = - I_{t}\dot{\phi^{2}}\sin\theta\cos\theta + I_{z}\dot{\theta}\sin\theta\left( \dot{\phi}\cos\theta + \dot{\psi} \right)\)

For torque free motion (gravity is only external force)

\(\dot{\psi} = \frac{I_{\mathrm{cg}} - I_{z}}{I_{z}}\dot{\phi}\cos\theta\)

note that \(I_{\mathrm{cg}} > I_z\) yields regular precession

while \(I_{\mathrm{cg}} < I_z\) yields retrograde precession

1.9 International Phonetic Alphabet and Morse Code

Character	Say	Morse Code
A	Alpha	• —
B	Bravo	— • • •
C	Charlie	— • — •
D	Delta	— • •
E	Echo	•
F	Foxtrot	• • — •
G	Golf	— — •
H	Hotel	• • • •
I	India	• •
J	Juliet	• — — —
K	Kilo	— • —
L	Lima	• — • •
M	Mike	— —
N	November	— •
O	Oscar	— — —
P	Papa	• — — •
Q	Quebec	— — • —
R	Romeo	• — •
S	Sierra	• • •
T	Tango	—
U	Uniform	• • —
V	Victor	• • • —
W	Whiskey	• — —
X	X-ray	— • • —
Y	Yankee	— • — —
Z	Zulu	— — • •
1	One	• — — — —
2	Two	• • — — —
3	Tree	• • • — —
4	Four	• • • • —
5	Fife	• • • • •
6	Six	— • • • •
7	Seven	— — • • •
8	Eight	— — — • •
9	Niner	— — — — •
0	Zee-ro	— — — — —

“1976 Standard Atmosphere Calculator.” n.d. Accessed August 21, 2022. https://www.digitaldutch.com/atmoscalc/.

Abbott, Michael M., and H. C. Van Ness. 1989. Schaum’s Outline of Theory and Problems of Thermodynamics. 2d ed. Schaum’s Outline Series. New York: McGraw-Hill.

Aeronautical Vestpocket Handbook. 1991. 22d ed. 1000 Marie Victorin Blvd. E. P.O.B. 10 Longueuil, Quebec Canada J4K 4X9: United Technologies Pratt & Whitney Canada. https://www.scribd.com/document/279045636/Aeronautical-Vestpocket-Handbook-Pratt-Whitney-22nd-Edition-Sep-1991.

Eshbach, Ovid W. 1936. Handbook of Engineering Fundamentals. Wiley Engineering Handbook Series, [1098] p. New York : London: Wiley ; Chapmann & Hall. //catalog.hathitrust.org/Record/001511835.

Jones, J.P., and G.A. Hawkings. 1960. Engineering Thermodynamics. John Wiley & Sons.

“Online Conversion - Convert Just about Anything to Anything Else.” n.d. Accessed August 21, 2022. https://www.onlineconversion.com/.

Potter, Merle C., and Craig W. Somerton. 1993. Schaum’s Outline of Theory and Problems of Engineering Thermodynamics. Schaum’s Outline Series. New York: McGraw-Hill.

Roberts, S.C. 1997. Aircraft Flying Qualities Testing. P.O. Box 658, Mojave, CA, 93501: National Test Pilot School.

SAWE Weight Engineers Handbook. 1976. Society of Allied Weight Engineers, Incorporated.

“SI Brochure - BIPM.” n.d. Accessed August 21, 2022. https://www.bipm.org/en/publications/si-brochure/.

“U.S. Survey Foot.” 2019. NIST, July. https://www.nist.gov/pml/us-surveyfoot.

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1. Common FTE conversions in boldface

2. solid angle measurement

3. Converting between force and mass (e.g. kg force to kg mass or pound force to pound mass) uses \(g = 32.174 \frac{ft}{s^2}\)

4. Fuel densities are temperature dependent

5. The foot is defined as exactly 0.3048 meters (“U.S. Survey Foot” 2019)

6. The SI defines the nautical mile as exactly 1852 meters. (“SI Brochure - BIPM” n.d.)