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nulrich(at)technq.com
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 Posted: Wed May 24, 2006 5:40 am Post subject: Cat fight |
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Math is beautiful, but more so when it's accurate  .
If you were calculating the speed increase for a car, you'd be pretty close
assuming that speed increases with the cube root of power, but it's not
quite true for an airplane.
The power required to overcome parasitic drag (that of the non-lifting
surfaces) increases proportionally to the cube of the velocity, but the
induced drag (that of the wing) actually decreases with increasing speed.
The lift required to maintain altitude remains the same, but the required
wing angle of attack decreases as the speed increases (lift is proportional
to the square of the speed) so the drag of the wing decreases.
Also, as you go faster, the advance ratio of your propellor increases, which
typically makes the propellor more efficient.
Of course, the overall result is that power required still increases
exponentially with speed, but it's not nearly as bad as the cube. How much
will depend a lot on where on the L/D curve you are, but for typical cruise
speeds in my Bonanza, adding 10% power results in about a 5% speed increase.
At just above best glide (max L/D) speed, where the drag curve is very flat,
adding 10% power results in a 9% increase in speed.
Nathan
Time: 08:27:05 AM PST US
From: Hopperdhh(at)aol.com
Subject: Re: Re: AeroElectric-List Digest: 7 Msgs -
05/22/06
Ah! I agree, I'm not a cat either, but a simple engineer. Let's see, drag
goes up as the square of speed so power required goes up as the cube of
speed.
(Power=force x velocity) Force in this case is the thrust required to
overcome the drag. Now, the cube root of .75 is 0.90856. So we should
expect
speed at 75 percent power to be 91 percent of the speed at 100 percent
power.
Isn't math beautiful?
Dan Hopper
RV-7A Flying 164 hours now. What a wonderful airplane!
In a message dated 5/23/2006 10:43:33 A.M. Eastern Daylight Time,
frank.hinde(at)hp.com writes:
Not to jump into the middle of so delicious a cat fight, but you guys might
be interested in this data. I have an insurance company database with
manufacturers specified horsepower, max speed, and 75% cruise speed numbers
for 440 (mostly American) light aircraft. The average horsepower is 220.5,
average top speed is 164.4 knots, and the average manufacturers claimed 75%
power cruise speed is 153.5 knots. That works out to 93.4% of the average
top speed.
Regards,
Lee...
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frank.hinde(at)hp.com
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Hopperdhh(at)aol.com
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| Posted: Thu May 25, 2006 4:00 am Post subject: Cat fight |
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Nathan, Kevin and Lee,
Very good replies. I'll admit that my assumptions are usually
oversimplified. You both (Nathan and Kevin) have made good points that could account for
the difference between my simple 91% and Lee's statistical 93.4%. Of course,
if we were behind the power curve the simple assumption I made would fall
completely out of the window, but you have taught me something here about
induced drag. Not being a trained aerodynamicist, those things didn't come to
mind while I was excitedly writing my response the other day.
My sincere thank you for setting me straight.
Back to electronics where things are much simpler!
do not archive
Dan Hopper
RV-7A flying about 165 hours
In a message dated 5/24/2006 9:42:06 A.M. Eastern Daylight Time,
nulrich(at)technq.com writes:
<nulrich(at)technq.com>
Math is beautiful, but more so when it's accurate .
If you were calculating the speed increase for a car, you'd be pretty close
assuming that speed increases with the cube root of power, but it's not
quite true for an airplane.
The power required to overcome parasitic drag (that of the non-lifting
surfaces) increases proportionally to the cube of the velocity, but the
induced drag (that of the wing) actually decreases with increasing speed.
The lift required to maintain altitude remains the same, but the required
wing angle of attack decreases as the speed increases (lift is proportional
to the square of the speed) so the drag of the wing decreases.
Also, as you go faster, the advance ratio of your propellor increases, which
typically makes the propellor more efficient.
Of course, the overall result is that power required still increases
exponentially with speed, but it's not nearly as bad as the cube. How much
will depend a lot on where on the L/D curve you are, but for typical cruise
speeds in my Bonanza, adding 10% power results in about a 5% speed increase.
At just above best glide (max L/D) speed, where the drag curve is very flat,
adding 10% power results in a 9% increase in speed.
Nathan
Time: 08:27:05 AM PST US
From: Hopperdhh(at)aol.com
Subject: Re: Re: AeroElectric-List Digest: 7 Msgs -
05/22/06
--> AeroElectric-List message posted by: Hopperdhh(at)aol.com
Ah! I agree, I'm not a cat either, but a simple engineer. Let's see, drag
goes up as the square of speed so power required goes up as the cube of
speed.
(Power=force x velocity) Force in this case is the thrust required to
overcome the drag. Now, the cube root of .75 is 0.90856. So we should
expect
speed at 75 percent power to be 91 percent of the speed at 100 percent
power.
Isn't math beautiful?
Dan Hopper
RV-7A Flying 164 hours now. What a wonderful airplane!
In a message dated 5/23/2006 10:43:33 A.M. Eastern Daylight Time,
frank.hinde(at)hp.com writes:
Not to jump into the middle of so delicious a cat fight, but you guys might
be interested in this data. I have an insurance company database with
manufacturers specified horsepower, max speed, and 75% cruise speed numbers
for 440 (mostly American) light aircraft. The average horsepower is 220.5,
average top speed is 164.4 knots, and the average manufacturers claimed 75%
power cruise speed is 153.5 knots. That works out to 93.4% of the average
top speed.
Regards,
Lee...
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