Climb Performance Analysis

[davidjh]

A critique of my understanding is asked for;

FAR Part 25 airplanes have six climb configurations each of which has a unique minimum climb gradient requirement. My study into the basic equations of energy theory and balance of forces in a climb leads me to the equation;

Sin (Flight Path Angle) = (Net Thrust minus Airplane Drag) divided by Airplane Weight = (Fn – D)/W.

This is for a constant true-airspeed climb. Gamma is often used as symbol for Flight Path Angle.

Since the airplane climbs at a constant CAS/KIAS there is a small correction factor needed for that scenario, so the equation becomes;

Sin(Gamma) + (1/g)(dV/dt) = (Fn – D)/W

Where g is the gravitational constant, and dV/dt is the change in true-airspeed with time during the climb.

So here is my first question; have I missed something in this derivation?

Next, two assumptions are made.

First; For the small angles involved at the limiting conditions (ie; the min gradient which ranges up to 0.032), the term Sin (Gamma) is equal to climb gradient.

Second; again at the limiting conditions, the speed change correction can be approximated by the value - 0.0007 to 0.0008 - for these angles and near-sea-level atmosphere. All but one of the six configs is with an engine inoperative so the rates of climb at the FAR limiting condition are small; 300ft/min to about 600 ft/min.

So, now my second and third question. Am I correct in these two assumptions?

Thanks.

 

[sailoday28]

Since the airplane climbs at a constant CAS/KIAS there is a small correction factor needed for that scenario, so the equation becomes;

Sin(Gamma) + (1/g)(dV/dt) = (Fn – D)/W

What is CAS/KIAS ?
Equation looks valid.
I wonder, how are Fn and D calculated? Since D with dV/dt=0 is a function of V? Otherwise, unless a slow transient, D can be a complicated function.

 

[davidjh]

sailoday28

CAS/KIAS - sorry, wrong to assume abreviations I'm familar with are familar to everyone else who participates. CAS = Calibrated Airspeed; KIAS = Knots,Indicated Airspeed. The Flight Manual will prescribe the speeds in KIAS which equates to a CAS by correcting for instrument and static port position error. So during a climb at a constant CAS the Vt(ie True Aispeed) will change.