AS309 Review Notes Exam I



AS309 Review Notes Unit I

A. Calculations

|Problem Type |Formulae |Comments |

| Steady State Climb |L + T sin r =W cos c |L = lift; D = drag; T = thrust; W |

| |T cos r = D + W sin c |= weight (all in #) |

| |r = p - c |c = climb angle |

| | |p = pitch angle |

| | |r = relative pitch angle |

| | | |

|Steady State Power Off Descent |D = W sin a |L = lift; D = drag; W = weight |

| |L = W cos a |(all in #) |

| |tan a = AA / GD |a = angle of descent |

| |GR = GD / AA s= 1 / tan a |max glide distance at min glide |

| | |angle and (L/D)max |

| | |(L/D)max = GR (glide ratio) |

|Steady State Turning Flight |G = L / W = 1 / cos ( |( = bank angle |

|L cos ( |L cos ( = W |CF is centripetal force in # |

|( L |CF = L sin ( |L = lift, W = weight (both in #) |

|L sin ( | |T ( D in SS turning flight (T = D |

| | |if pitch angle is zero) |

| | |G is g force (no units) |

|W | | |

|Convert Between nm/hr and ft/sec |3600 sec/hr |Use of improper units in a formula is a |

| |6076 ft/nm |common error. So is converting incorrectly|

| |x ft/sec = x (3600 /6076) kts |between kts (nm/hr) and ft/sec. |

| |y kts = y / (3600/6076) ft/sec | |

|Turn Radius |r = V2 / (g tan () |r = turn radius in feet |

| |3600 sec/hr |g = 32.2 ft/sec2 |

| |6076 ft/nm |( = bank angle |

| |x ft/sec = x (3600 /6076) kts |V = TAS in ft/sec |

| |y kts = y / (3600/6076) ft/sec | |

|Turn Rate |TR = 180 g tan ( / (( V) |TR = turn rate in deg/sec |

| | |G = 32.2 ft/sec2 |

| | |( = bank angle |

| | |V = TAS in ft/sec |

|Propeller RPM |RPM = 60 TS / (2 ( r) |RPM = revolutions / minute |

| |RPM = 60 TS / (( d) |TS = tip speed in ft/sec |

| | |r = prop radius in ft |

| | |(d = prop diameter = 2r) |

|Acceleration on Takeoff |F = m a = (W/g) a |F = thrust in # |

| | |W = weight in # |

| | |g = 32.2 ft/sec2 |

| | |a = acceleration in ft/sec2 |

B. Other Formulae of Interest (most are discussed later):

• A1V1 = A2V2, A ( r2

• H = P + q

• TAS = EAS / ((

• (= P / P0, ( = T / T0, ( = ( / (0

• ( = ( / (

C. Implications of Formulae.

You should know what each formula “means.” For example

• L < W in Steady State (SS) climbing flight

• Turn radius directly proportional to V2

• Turn rate inversely proportional to V

• G force proportional to bank angle ( , 0o ( ( < 90o

• No SS level 90o bank angle turn is possible

• Doubling TAS or results in

1. Increase in turn radius by a factor of four

2. Decrease in turn rate by a factor of two

• If bank angle ( < 45o is doubled, G force increases by cos (/ cos 2( (not a constant factor).

There are many similar problems that might be posed.

D. Properties of the Atmosphere.

Pressure:

• P0 = 2116 #/ft2 = 14.69444 #/in2.

• Pressure ratio ( = P / P0.

• About ½ the atmosphere by weight lies below 18,000’ in a standard atmosphere.

• That is, (18,000’ ( 0.5.

Temperature.

• T0 = 59o F = 15o C = 519o R = 288o K.

• Temperature ratio ( = T / T0. Must use absolute temperatures (K or R) to calculate (.

• Temperature decreases 2o /1000’ (almost exactly) to the tropopause (36,089’), then levels off at –69.6o F until entering the stratosphere.

• ( at the tropopause (0.752) is about ¾ of ( at SL.

Density.

• Density ( is mass/unit volume (slugs /ft3).

• Density is a function of temperature and pressure.

• (0 = 0.002377 slugs/ft3.

• (22,000’ = 0.001183 slugs/ft3, about half that at sea level.

• Density ratio ( = ( / (0.

• It follows that (22,000’ = 0.001183 / 0.002377 ( 0.5 (check standard atmosphere table to confirm).

• That is, half the atmosphere by density lies below 22,000’ in a standard atmosphere.

• ( = ( / ( is a very important and useful relationship. (Reflects the fact that density is a function of both pressure and temperature.)

• Suppose P decreases and T remains the same. What happens to (? (Since ( = ( / (, and since ( decreases if P decreases while ( remains constant, ( must decrease.)

E. Altitude Measurement

• Indicated altitude (IA) is read on altimeter (assume no instrument error).

• Pressure altitude (PA) is IA corrected for non-standard pressure.

• Pressure altitude correction is 1000’ / inch of Hg in lower altitude.

• Subtract correction for higher than standard pressure; add correction for lower than standard.

• Density altitude (DA) is PA corrected for non-standard temperature.

• Must correct for both P and T to get density altitude.

• Density altitude used for performance calculations.

F. Pitot-Static A/S Indicators.

• If no air compression, A1V1 = A2V2 when air flows through a conduit of varying x-sectional areas A1 and A2. V1 and V2 are the corresponding air velocities.

• Distinguish static pressure (P) from dynamic pressure (q).

• q = (V2/2, where V is TAS in ft/sec. (q is measured in #/ft2 just like static pressure.)

• Bernoulli’s Principle: H (total pressure) = P (static pressure) + q (dynamic pressure), assuming no air compressibility.

• In short: H = P + q = P + (V2/2.

• Bernoulli’s Principle is the scientific basis for the pitot-static airspeed indicator, the carburetor, and the airfoil, among other devices.

• A/S indicator measures the difference between total pressure H and static pressure P to “calculate” dynamic pressure q, then displays the result in knots.

• That is, a pitot-static system calculates the ratio H / P = H / (H – q) and displays the result in knots. The value of q can be inferred from the ratio H / P.

• H is read at the stagnation point of the pitot tube. P = H – q is read at the system’s static port.

• You should be able to draw and explain the diagram of the pitot-static A/S system given in the notes.

G. Airspeed Measurement.

• Indicated air speed (IAS) is read on the A/S indicator

• Calibrated air speed (CAS) is IAS corrected for pitot-static system error.

1. Instrument error.

2. Error due to airflow disruption, especially at static port.

• Equivalent air speed (EAS) is CAS corrected for compressibility effect.

• IAS to CAS correction is aircraft model dependent. Correction is usually small.

• CAS to EAS correction is aircraft model independent.

• Compressibility causes the A/S indicator to read too high, so always subtract the correction from CAS to get EAS.

• Largest CAS to EAS corrections in subsonic flight regime are at 20-40M altitude and 300-500 kts. Correction can exceed 25 kts, i.e. can be large compared to IAS-CAS correction.

• True airspeed (TAS) is EAS corrected for non-standard density.

• TAS = EAS / (( gives the relationship between EAS and TAS.

• At high altitudes, TAS can be twice as high as EAS.

• A/C generates lift and drag responds to controls according to EAS, not TAS.

• TAS is of interest to pilots primarily when they are functioning as navigators. TAS has little or nothing to do with the way an aircraft flies or handles.

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