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Turn radius

To calculate radius of turns, use this formula velocity^2 / (9.81 * tan(bankAngle)) where velocity is in m/s and bankAngle in whatever the tan function takes

Altitude loss during a turn while gliding

Percentage of a full turn when doing an "impossible turn" (180º followed by two 30º turns): (180+30+30)/360 = 66,66666% Radius of turn at 45º and 76kt: -> To make a safe turn at 45º the airspeed has to be increased to at least 1.44*Vs (1.5*Vs is recommended) (velocity*1.44)^2 / (9.81 * tan(bankAngle)) = 323m = 1060ft Circumference of circle: 2 * π * 323m = 2030m Distance covered during circle (2780m is the glide distance per 1000ft height loss for the C172): 2030m * 67% = 1360.1m (or 49% of 2780m) Height loss to glide distance (convert to actual feet height loss): 1000ft * 0.49 = 490ft

Comparing against numbers from a brilliant AOPA article yields an error of about 8% (450ft vs. 490ft). While off by a bit, it errors on the side of caution and provides a reasonable safety margin.

Using 1.5\*Vs yields a height loss of 530ft which is a whopping ~8% increase from 1.44\*Vs!

Calculating climb factor

Given climb rate and airspeed:

climb:
    rate: 3.09
    speed: 79

The speed in KIAS (ignorantly skipping KCAS) is equal to KTAS in a standard atmosphere at MSL. Speed converted to m/s: 40,67m/s Duration to climb to 1000m: 1000m / 3.09m/s = 323,62s Distance travelled diagonally: 40,67m/s * 323,62s = 13161.6254m Calculating the ground track via pythagoras: sqrt(1000m^2 + 13161.6254m^2) ~= 13200m Converting to a slope: 13200m / 1000m = 13.2 For each X height gained, slope * X ground distance is covered.

Example: Climbing 2.000ft -> 2000ft * ~13.2 = 26.400ft = 4.344879nm POH: 4nm

More comparisons:

Height Calculation POH
1000 2.17244 2
2000 4.344879 4
3000 6.517319 6
4000 8.689758 8

=> It appears that the POH is rounding and that past 3000ft the reduced climb-rate is affecting accuracy (albeit into the direction of more tolerance in terms of having an engine failure)

Calculating glide factor

Calculate ratio between 1000ft (304.8m) and distance (example C172): 2800m / 304.8m = 9.18

TODOs

  • Write a tool to generate "derived" values
    • Climp factor (e.g. 13.2 for C172)
    • Glide factor (e.g. 9.18 for C172)