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Ed Anderson wrote:
Gee, Ernest, I don't know.
But, perhaps we can get a handle on it starting with F = m*a.
lets take one cubic foot of air and assume no losses in accelerating it from 0 to 150 Mph. Now we need a time interval and it has to be around 1 rpm (one revolution of the blades) so that is approx 60/7000 = 0.00857 sec/rev. Since we want 600 cfm of air to flow at 150 mph we need to have the blower flow 600/7000 = 0.857 CF per revolution. 0.857 * 7000 = 600 CFM - checks!
At 7000 rpm the e shaft needs 0.00857 sec per rev. So we want to accelerate 0.857 CF of air from zero to 150 mph in 0.00857 seconds.
A cubic foot of air has a mass of 0.0765 lbs at sea level. So M = 0.0765 lbs. We need to accelerate it to 150 mph or 220 ft/sec velocity in 0.0086 seconds. So dV/dt = A = 200 ft/sec/0.0086 sec = 25,666 ft/sec^2 or 25666/32 = 802 Gs acceleration. Therefore F = m*a = 0.0765 * 25666 = 1963.5 lbf/sec = 1963.5*0.001818 = 3.56 HP Since we continuously need to accelerate that amount of air it would appear that not counting for any losses that you would need approx 3.56 HP or approx 1/2 of the amount your increase air supply might contribute to power increase in the engine.
I've been double checking your numbers, and I think I have a correction.
-"We want to accelerate 0.857 CF of air from zero to 150 mph in 0.00857 seconds" and "A cubic foot of air has a mass of 0.0765 lbs at sea level. " So M = .857 * .0765 = .0656
- You change the velocity from 220 ft/sec to 200ft/sec, but I think this was just a typo, and you're actually doing the numbers in a seperate calculator. The numbers I'm getting don't come up exactly with what you have...but close.
- With the correction, F=m*a=0.0656*25670=1684 lbf/sec * 0.001818 => 3.06 Hp.
This is for delivery of 600CFM. 300CFM would use half of that. Even 50% efficiency should yield significantly more power than is used.
I did have some numbers before, but they're just marketing numbers and therefor offer no guarantee of resembling reality. In fact, Tanaka's claims appear to be very suspect.
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