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