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Date: Wed, 19 Dec 2007 13:06:41 -0500
From: Ernest Christley <echristley@nc.rr.com>
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To: Rotary motors in aircraft <flyrotary@lancaironline.net>
Subject: Re: [FlyRotary] Re: Supercharging
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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.