OR

CONVERSIONS:

1 foot = 0.3048 meters km/h -> m/s = divide by 3.6 Specific fuel consumption. To get in metric, divide by 1980000 then 0.3048. BASICS (CH4 SUMMARY):

Equation of state:

For compressible flow:

For incompressible flow (V < 100m/s OR M < 0.3):

Mach number at altitude: where p1 is ambient air pressure (from table) and p0 is pressure at wing (ie measured by pitot tube or similar). p181 Anderson.

ISENTROPIC RELATIONSHIP: temperatures in kelvin, found in ISA table below.

OR

SKIN FRICTION:

and

Incompressible turbulent boundary layers:

ZERO LIFT DRAG COEFFICIENT:

Theoretical prediction of transition from laminar to turbulent layers is very difficult. Experimentation is needed. Critical reynold's number finds the theoretical transition point between laminar and turbulent air flow.

LIFT:

At higher speeds: (c_l,0 is found from the NACA charts)

DRAG:

MOMENT:

STALLING:

is is is is

higher for greater weight lower for greater lower for greater wing area lower for greater air density

MAXIMUM VELOCITY:

PRESSURE COEFFICIENT: Describes how pressure on surface of wing deviates from freestream pressure. Cp is plotted upside down, with negative axis pointed up.

For

For

QUARTER CHORD MOMENT:

COEFFICIENT OF DRAG (FINITE WING) (e is Oswald efficiency factor)

COEFFICIENT OF LIFT (FINITE WING) (steady, level flight)

LIFT SLOPE FOR A FINITE WING:

Total Force Normal:

STEADY AND LEVEL FLIGHT:

Inverted:

for lift to drag ratio.

POWER REQUIRED

POWER AVAILABLE: For prop planes: where P is total power available from both engines. For jets:

THRUST REQUIRED:

ALTITUDE EFFECTS:

so

p1 is ambient pressure (from table), p0 is pressure on wing (ie from pitot tube) page181

RATE OF CLIMB:

GLIDING FLIGHT: Where theta is glide angle, W is weight.

RADAR:

RANGE (get ready): (props)

c = specific fuel consumption (must be in N/(J/s) (s)) (jets) ENDURANCE: Maximum endurance is found at maximum

(props)

(jet)

LIFT OFF ROLLING DISTANCE:

where

Remember, b is wingspan. h is height of the wing above ground.

Get Vlo first, then multiply by 0.7. Calculate drag and lift from this velocity, then sub into the equation above. IF THRUST IS LARGE:

LIFT OFF VELOCITY

TOUCHDOWN VELOCITY:

where V(infinity) is 0.7Vt Then

MAXIMUM AERODYNAMIC RATIOS (TO FIND MAX RANGE AND MAX ENDURANCE): These replace

in the range and endurance equations given above.

CD0 and Cl maxes:

WEIGHT OF FUEL: Avgas doesn't have the same density as water, so you cannot just multiply by 9.81 to get its weight. You must multiply it by its density, which is 5.64lb per US gallon. Convert this by multiplying by 0.264172052 then 0.4536 to get metric.

LONGITUDINAL STABILITY AND BALANCE: 1. The aircraft has longitudinal static stability when:

2. The aircraft is balanced when the trim angle of attack range.

falls within reasonable flight

// IMPORTANT

NEUTRAL POINT: The neutral point is where the aircraft is statically neutral, the cg location for hn for which gradient is zero.

LEVEL TURNS: In this situation, is bank angle. To stay level, the lift produced at this bank angle must balance the weight.

so For circular turns: where R is radius of turn.

The higher the lift to weight ratio is, the tighter the turn. The rate of turn is angular velocity:

high load factor and low velocity both produce high rates of turn and tight turns. PULL-UP MANOUEVRE: This is like a level turn, but on the vertical axis. Pulling up on the stick.

and

again, where n is the load factor. See above for its equation.

PULL DOWN MANOUEVRE: Seen in high performance aircraft, where n is very large.

MAXIMUM LOAD FACTOR:

ISA table: Pressure Kinematic -pThermal Speed of Elevation Temperature Viscosity (bar NOT RelativeDensity Conductivity Sound -z-T-νTO BE - ρ/ρo -k-c(m) (K) x 10-5 USED FOR (kW/m K) (m/s) (m2/s) Cp) -2000 301.2 1.2778 1.2067 1.253 2.636 347.9 -1500 297.9 1.2070 1.1522 1.301 2.611 346.0 -1000 294.7 1.1393 1.0996 1.352 2.585 344.1 -500 291.4 1.0748 1.0489 1.405 2.560 342.2 0 288.15 1.01325 1.0000 1.461 2.534 340.3 500 284.9 0.9546 0.9529 1.520 2.509 338.4 1000 281.7 0.8988 0.9075 1.581 2.483 336.4 1500 278.4 0.8456 0.8638 1.646 2.457 334.5 2000 275.2 0.7950 0.8217 1.715 2.431 332.5 2500 271.9 0.7469 0.7812 1.787 2.405 330.6 3000 268.7 0.7012 0.7423 1.863 2.379 328.6 3500 265.4 0.6578 0.7048 1.943 2.353 326.6 4000 262.2 0.6166 0.6689 2.028 2.327 324.6 4500 258.9 0.5775 0.6343 2.117 2.301 322.6 5000 255.7 0.5405 0.6012 2.211 2.275 320.5 5500 252.4 0.5054 0.5694 2.311 2.248 318.5 6000 249.2 0.4722 0.5389 2.416 2.222 316.5 6500 245.9 0.4408 0.5096 2.528 2.195 314.4 7000 242.7 0.4111 0.4817 2.646 2.169 312.3 7500 239.5 0.3830 0.4549 2.771 2.142 310.2 8000 236.2 0.3565 0.4292 2.904 2.115 308.1 8500 233.0 0.3315 0.4047 3.046 2.088 306.0 9000 229.7 0.3080 0.3813 3.196 2.061 303.8 9500 226.5 0.2858 0.3589 3.355 2.034 301.7 10000 223.3 0.2650 0.3376 3.525 2.007 299.8

10500 11000 11500 12000 12500 13000 13500 14000 14500 15000 15500 16000 16500 17000 17500 18000 18500 19000 19500 20000 22000 24000 26000 28000 30000

220.0 216.8 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 218.6 220.6 222.5 224.5 226.5

Geo potential Altitude Temperature above Sea -tLevel o ( C) -h(m) -1000 21.50 0 15.00 1000 8.50 2000 2.00 3000 -4.49 4000 -10.98 5000 -17.47 6000 -23.96 7000 -30.45 8000 -36.94 9000 -43.42 10000 -49.90 15000 -56.50 20000 -56.50

0.2454 0.2270 0.2098 0.1940 0.1793 0.1658 0.1533 0.1417 0.1310 0.1211 0.1120 0.1035 0.09572 0.08850 0.08182 0.07565 0.06995 0.06467 0.05980 0.05529 0.04047 0.02972 0.02188 0.01616 0.01197

0.3172 0.2978 0.2755 0.2546 0.2354 0.2176 0.2012 0.1860 0.1720 0.1590 0.1470 0.1359 0.1256 0.1162 0.1074 0.09930 0.09182 0.08489 0.07850 0.07258 0.05266 0.03832 0.02797 0.02047 0.01503

3.706 3.899 4.213 4.557 4.930 5.333 5.768 6.239 6.749 7.300 7.895 8.540 9.237 9.990 10.805 11.686 12.639 13.670 14.784 15.989 22.201 30.743 42.439 58.405 80.134

1.980 1.953 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.952 1.968 1.985 2.001 2.018 2.034

Acceleration of Gravity -g2 (m/s )

Absolute Pressure -p4 2 (10 N/m )

Dynamic Density Viscosity -ρ-μ-1 3 -5 (10 kg/m ) (10 2 N.s/m )

9.810 9.807 9.804 9.801 9.797 9.794 9.791 9.788 9.785 9.782 9.779 9.776 9.761 9.745

11.39 10.13 8.988 7.950 7.012 6.166 5.405 4.722 4.111 3.565 3.080 2.650 1.211 0.5529

13.47 12.25 11.12 10.07 9.093 8.194 7.364 6.601 5.900 5.258 4.671 4.135 1.948 0.8891

1.821 1.789 1.758 1.726 1.694 1.661 1.628 1.595 1.561 1.527 1.493 1.458 1.422 1.422

297.4 295.2 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 295.1 296.4 297.7 299.1 300.4 301.7

25000 30000 40000 50000 60000 70000 80000

-51.60 -46.64 -22.80 -2.5 -26.13 -53.57 -74.51

9.730 9.715 9.684 9.654 9.624 9.594 9.564

0.2549 0.1197 0.0287 0.007978 0.002196 0.00052 0.00011

0.4008 0.1841 0.03996 0.01027 0.003097 0.0008283 0.0001846

1.448 1.475 1.601 1.704 1.584 1.438 1.321

BOOK SOLUTION PAGES AND THE QUESTIONS THEMSELVES: CH4 - Basic Aerodynamics: SUMMARY PAGE 247. p164 - Compute mach number given altitude, velocity. p165 - nozzle flow p168 - mercury manometer in a subsonic wind tunnel. Calculate airflow velocity. p178 - pitot tube on cessna wing. Given air temp, pressure in pitot tube, altitude. Compute airspeed. p181 - pitot tube question, calculate Mach number of aircraft, given metric numbers for ambient air temp, pressure in pitot tube, altitude. p187 - isentropic flow over airfoil. Given free-stream pressure, velocity, density and pressure at point A of airfoil. What is mach # and velocity at point A? p196 - design a supersonic wind tunnel that has mach 2 flow @ sea level conditions in test section. What area ratio is required. p198 - isentropic flow in a rocket engine. Given temperature, pressure, specific gas constant R and gamma plus area of nozzle. Find velocity at exit + mass flow through nozzle. p212 - boundary layer thickness and drag force on plate, assuming laminar flow. Given flow velocity and dimensions of plate. p213 - calculate local shear stress at locations 1 and 5cm from leading edge of plate given in question above. p216 - same flow over same plate, now assume boundary layer COMPLETELY TURBULENT. Calc boundary layer thickness at trailing edge and drag force on plate. p219 - Supersonic fighter. Assume infinitely thin wing. altitude given, boundary layer is turbulent. Estimate shear stress 2ft downstream of leading edge.

p222 - Find skin friction drag of wright flyer, given S, V(infty) and transition reynolds number. p229 - Given name of airfoil, mointed in test section of wind tunnel. Spans entire tube. Given length and width. Induced drag is zero, Velocity of wind is given, profile drag given (angle of attack is zero). Calculate drag on airfoil due to skin friction. Calc profile drag due to flow separation.

CH5 - Airfoils, Wings and Other Aero dynamic Shapes: SUMMARY PAGE 390. p275 - Model wing in wind tunnel. Given airfoil number and chord length. Velocity in tunnel is given and is at sea level. If wing is at 4 degrees angle of attack, , the lift, drag and moments around the quarter chord, per unit span. p276 - same wing in same flow, pitched to angle such that lift per unit span is 700N. What is the angle of attack, and what angle of attack must the wing be pitched to to obtain L = 0 Newtons? p276 - Airfoil number given, again, flush with the walls. At zero angle of attack, drag = 34.7N. Flow velocity is 97m/s, standard sea level conditions. Chord = 0.6m, wingspan = 1m. Hence 34.7N is drag per unit span. Calculate drag coefficient. p277 - Split flap question, deflected at 60 degrees. p283 - Pressure point on wing given, velocity of aircraft given, altitude given. Find pressure coefficient of this point on wing. p283 - Low subsonic wind tunnel. Flow velocity given and pressure at a point on airfoil given. What is the pressure coefficient. p283 - Flow velocity is increased so that the free-stream Mach number is 0.6. p284 - aircraft flying at velocity of 100m/s at standard altitude of 3km. Pressure coefficient at a point on plane is -2.2. What is pressure at this point? p284 - Two different points on surface of airplane wing at 80m/s. Pressure coefficient given for point one, flow velocity given. Pressure coefficient at point 2 given. Incompressible flow. Calc velocity at point two. p289 - Airfoil with chord length c and running distance x. Leading edge located at x/c = 0, trailing edge at x/c = 1. PRessure coefficient variations over upper and lower surfaces are given (three equations with limits). Calculate the normal force coefficient.

p291 - NACA 4412 airfoil at angle of attack 4 degrees. If free-stream mach number is 0.7, what is the lift coefficient? p298 - Airfoil given, plus graph of pressure coefficient distribution over its surface, at Re = 3.65e6. What is the critical mach number of this airfoil at zero angle of attack? p315 - Thin supersonic airfoil with chord length c = 5 ft in a Mach 3 freestream at altitude 20,000ft. Angle of attack is 5 degrees. Calculate lift and wave drag coefficients, and lift and wage drag per unit span. p317 - Supersonic fighter; S = 19.5m squared. Steady, level flight (L=W). Weight is 7262kgf. Calculate its angle of attack at Mach 2 at sea level and 10km altitude. p318 - Flying at steady, level flight, mach 2 at an altitude of 10km, pilot suddenly pitches the airplane to an angle of attack of 10 degrees. Calculate instantaneous lift exerted on the airplane. This also shows the g forces on the pilot. p328 - Fighter airplane with S = 170ft^2. Generates 18,000lb of lift. Flight velocity is 250mi/h at sea level. Calculate the lift coefficient. p329 - Wingspan of plane in previous question is 25.25ft. Calculate the induced drag coefficient and induced drag. Assume e = 0.8. p329 - A flying wing with wing area of 206m^2, AR = 10, e=0.95, and NACA 4412 airfoil. Weight of plane given as 7.5e5N. Density altitude is 3km and flight velocity is 100m/ s. calculate total drag on aircraft. p330 - North american p-51 mustang. NACA airfoil given. Weight given. S given. Wing span given. e = 0.99. Altitude given. Max velocity given. At this altitude and velocity, calculate and compare the induced drag and profile drag of the wing. At sea level, calculate the induced drag and profile drag at 140mph.. p335 - AR = 10, NACA airfoil given. Assume Re = 5e6. e = e1 = 0.95. If wing at 4 degrees angle of attack, calculate CL and CD (finite wing). p336 - Given V = 30mi/h, calculate the induced drag on the wings, Assume e = 0.93. p355 - Full load of fuel, airplane weighs 10,258kg. Empty weight is 6071 kg. S = 18.21m^2. Thin wing, CLmax = only 1.15 because of thin wings. Calculate stalling speed at standard sea level, when fuel tanks are full and empty. p357 - Boeing 727 with low stalling speed. Max lift coefficient of 3, weight of 160,000lb, S = 1650ft^2. Calculate stalling speed.\ p370 - Can an airfoil produce lift when it is flying upside down? Yes, but not effectively. Two naca airfoils shown. For an angle of attack of 6 degrees, obtain the lift coefficient for each.

CH6 - Elements of Airplane Performance: SUMMARY PAGE 522. p410 - Calculate the Thrust Required Curves at Sea Level for these two planes given. p415 - Calculate the maximum velocity of CJ-1 at sea level. p420 - Calculate the power-required curves for the CP-1 at sea level and the CJ-1 at an altitude of 22,000ft. p429 - Given a power required curve at 22,000 ft, obtain the CJ-1 power-required curve at sea level. p436 - Calculate Rate of Climb (R/C) versus velocity at sea level for the CP-1 and CJ-1. p440 - The maximum lift-to-drag (L/D) ratio for the CP-1 is 13.6. calculate the minimum glide angle and the maximum range measured along the ground covered by the CP-1 in a power off glide that starts at an altitude of 10,000ft. p442 - For the CP-1, calculate the equilibrium glide velocities at altitudes of 10,000 and 2000ft, each corresponding to the minimum glide angle. p444 - Calculate the absolute and service ceilings for the CP-1 and the CJ-1. p447 - Calculate and compare the time required for the CP1 and CJ1 to climb to 20,000ft. p454 - Calculate the maximum range and maximum endurance for the CP-1. p459 - Calculate the maximum range and maximum endurance for the CJ-1 (jet). p463 - calculate (CL/CD)max and (CL^(3/2)/CD)max for the CP-1. p463 - calculate (CL^(1/2)/CD)max and (CL/CD)max for the CJ-1. p469 - Airplane with C_D,0 = 0.0025, AR = 7.37 and e=0.8. Aircraft is flying such that CL = 0.228. Calculate the ratio of lift to drag (L/D) at this condition. p474 - Estimate the liftoff distance for the CJ-1 at sea level. Assume paved runway ( ). Assume CL,max during ground roll is limited to 1.0. The wings are 6ft above the ground. p478 - Estimate the landing ground roll distance at sea level for the CJ-1. No thrust reversal used, though spoilers are used so that L=0. Spoilers increase CD,0 by 10%. Fuel tanks are empty, so neglect weight of fuel. Max lift coefficient with flaps fully deployed is 2.5. p502 - Using CP-1 airplane of previous examples, lets assume that its been changed to a UAV. Less weight. In this case, evaluate Vmax at sea level, maximum R/C at sea level,

maximum range, maximum endurance at sea level. Weights of people and equipment removed total 880lb. p505 - Conventional plane (L/D)max = 9, UCAV (L/D)max = 25. At the same flight velocity, compare the turn radius and turn rate for these two aircraft.

CH7 - Stability and Control SUMMARY PAGE 586. p550 - Given wing-body combination, aerodynamic centre (ac) lies 0.05 chord length ahead of the CG. The momenbt coefficient about the aerodynamic center is -0.016. If CL is 0.45, calculate the moment coefficient about the center of gravity. p551 - L=0 at angle of attack -1.5 degrees. At 5 degrees angle of attack, CL = 0.52. @ 1.0 degrees and 7.88 degrees, CMs about CG are measured as -0.01 and 0.05 respectively. CG is located at 0.35c. Calculate the location of the aerodynamic center and the value of . p556 - Aerea and chord of wing are 0.1m^2 and 0.1m respectively. Assume horizontal tail is added to model. Distance from CG to tac is 0.17m. St = 0.002m^2. Tail setting angle is 2.7 degrees, tail lift slope is 0.1 per degree. Epsilon zero is 0, partial epsilon, partial alpha = 0.35. If angle of attack is 7.88 degrees, calculate p558 - Consider wing-body-tail wind tunnel model in previous question. Does this model have longitudinal static stability and balance? p560 - From the model in previous questions, calculate the neutral point location. p561 - From previous question's model, calculate the static margin. p570 - Full size airplane with the same aerodynamic characteristics as the model in the previous questions, S = 19m^2, W = 2.27e4N, elevator control effectiveness is 0.04. Calculate the elevator deflection angle necessary to trim airplane at vel of 61m/s at sea level. p576 - Consider airplane in example 7.8. Its elevator hinge moment derivs are XYZ. Assess the stick-free static stability of this airplane.