Cold weather climb performance: fact or fiction?

[bookworm]

Keith

I think this TAS cubed thing is just a lack of clarity about what we're holding constant and what we're considering as a variable. We're probably saying the same thing in different ways.

Neglecting compressibility, and using a slight variant on your terminology:

dynamic pressure = 1/2Rho(TAS)squared = 1/2Rho_standard(CAS)squared

(where Rho_standard is a reference constant, density at ISA SL)

or TAS = d * CAS where d is the square root of the density ratio.

So

Drag = Cd * dynamic pressure * area

and

Power required = Drag * TAS

So you can write that as:

Cd * 1/2Rho_standard(CAS)squared * TAS * area

in other words proportional to (retaining density as a variable)

CAS squared * TAS

You can, if you want, write this as

Power required is proportional to CAS cubed * d

or you can write it as

Power required is proportional to TAS cubed / d squared

But for a constant CAS climb, the key is that the d comes in once not three times.

I think the complex shape of the drag curve is a bit of red herring, isn't it? Since lift depends on speed through the dynamic pressure too, the a point at constant CAS on the curves represents a particular drag-to-lift ratio, and therefore, for an aircraft of a particular weight a particular drag-to-weight ratio, regardless of density ratio. Turning that into a power required involves multiplying by the TAS or d only once.

hawk

I think Keith answered this the first time round, but let me share my understanding of his explanation by putting it another way. The thrust available depends explicitly on both temperature and TAS. Since TAS also depends on temperature for a constant CAS, there is also an indirect dependence on temperature.

If thrust is flat-rated, it means that the explicit dependence on temperature is removed. The static thrust (TAS = CAS = 0) will not depend on temperature. But for non-zero CAS, there is still that indirect temperature dependence. Thus the thrust available at climb CAS does vary with temperature even for a flat-rated engine.