Mailing List lml@lancaironline.net Message #41870
From: Fred Moreno <fredmoreno@optusnet.com.au>
Sender: <marv@lancaironline.net>
Subject: Cooling Drag - Error!
Date: Mon, 30 Apr 2007 23:17:13 -0400
To: <lml@lancaironline.net>

I warned you guys that I was getting old and forgetful.

 

I wrote previously that a rough rule of thumb for small changes is that a 2% drag decrease will yield a 1% speed increase.  Wrongo!  That is a simplification of the fact that drag goes as velocity squared which is not the full story.

 

What I wrote is true only when THRUST is constant, as with a jet engine.  For our piston engines, POWER is constant (more or less, fixed conditions). 

 

Power = thrust times velocity.   (This is a definition, or if you prefer, one of the fundamental laws.  Sorry.)

 

Recall Thrust = Drag

 

For constant Power,

 

Thrust goes like  1/Velocity. 

 

When you go faster, you make less thrust but also make more drag.  (When you go faster, your variable pitch prop bites more air to advance farther on each rev, but in so doing it makes less thrust consistent with the law that power = thrust times velocity.)

 

This means that for piston engine airplanes, power goes like velocity cubed, not velocity squared which is the error implied by my rule of thumb.

 

Simplified (“linearized” for you math buffs) this means for small changes the correct statement is:

 

It takes a 3% drag reduction to get a 1% speed increase.

 

Alas.

 

You get a tiny bit more power arising from the slight increase in ram pressure which translates into a tiny increase in manifold pressure, but not much.  I calculated that if you are at 9000 feet, ambient pressure about 21 in. HG, and you get full ram pressure into the intake manifold (you are getting this, aren’t you?) to give about 23 inches of manifold pressure, then a 3% speed increase gives you about 0.1% more power.

 

If you slog through all the math and take out the linear effects and assume I made no more errors (big assumption) the bottom line for a 10% drag decrease (our maximum goal for aspirated airplanes, 9000 feet, 230 knots TAS) you get a 3.3% increase in speed (which means the 3% rule is pretty good). 

 

Or about 7.7 knots. 

 

If you start with a particularly leaky cowl, lots of air gushing out the spinner-cowl gap, and set of leaky baffles, you might get a bit more.  But that seems to be it folks.

 

Fanatics will still persist for that last knot.  Those extra knots get more and more expensive, but you already knew that. J

 

Fred Moreno

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