I think you need to adjust from raw displacement at 0 PSIG to the portion of the displacement that remains after the air charge has been compressed to the output pressure. After all, until the pressure in the cylinder reaches the pressure in the tank, no air will flow through the check valves into the tank.
Your math for swept volume looks o.k. However, is your rating in CFM at some pressure? Also, you're not accounting for compression ratio. The less compression ratio, the less efficiency. The volume you swept loaded at ~14.7 psia at ambient temp. It exhausts at the tank back pressure and a higher temperature, and that volume between the piston and the reed valve at tdc re-expands, limiting the amount of air sucked in. (Based on that, I guess good design would minimize that volume by placing the valves very close to the pistons at tdc.)
No, I didn't calculate it. I'd have to dig out thermo texts and I think I chunked them. Just thinking about it makes my head hurt.
If I have this correct, assuming 90 PSIG output pressure you need 7:1 compression to get to output pressure where you actually feed into the tank. 3.5" stroke / 7 = .5" output stroke * 2 cylinders = 1" effective output stroke * 12.56 square inches cylinder bore = 12.56 CFM @ 90 PSIG (with some rounding error and assuming minimal dead air space between the cylinder and the valves).
When the crankshaft speed and piston displacement volume are calculated, that result is generally referred to as: free air displacement, meaning pressure doesn't enter into the calculation, (essentially the same as the cubic inch or liter, or CC displacement in engines).
If the pump was used to inflate a very thin, empty/collapsed plastic bag without reaching the point of stretching the bag, the results would be similar.
Does it really run 900 rpm? That would take like a 10 or 15 HP motor to deliver 90 psi. Maybe you have someth> However, is your rating in CFM at some pressure?
No, no, no. Please don't start up this old canard. Compressor CFM is measured in FREE AIR, not compressed. When a compressor pumps one "CFM" (cubic foot per minute), that means the intake port inhales one cubic foot of "free air" (air at atmospheric pressure, which is 0 psig) every minute.
The driving pulley is 5-1/2" and the driven pulley is 19" and the engine runs between 2200 and 3000 rpm depending on how the variable speed control is set. So yes, I can drive the pump at 900 rpm, and yes, 900 rpm is the max speed that this air pump (a Quincy model 244) can run.
Swept volume (not compressed volume) would be 1/2 half of Grant's calculation. Assuming a single acting piston there would be only 1/2 active stroke per cyclinder per revolution or 900 total strokes per minute.
Don't worry about it. I've seen ratings on machines at the stores that have been done by high dollar engineers, and they're farther off than yours.
How do you make a crankshaft that only moves the piston up every other rev?
Or is it that they both go up each rev but the valves only close on one or the other?
Actually, a factor of 2 is probably about close. Back in the mid-90s I was told that this compressor is capable of about 18 CFM IIRC. And half of 45 would be
22.5 which if the ACFM (at some normal condition) were 18 would give a volumetric efficiency of 80% which isn't an unreasonable number.
Grant
Robert Sw> Swept volume (not compressed volume) would be 1/2 half of Grant's calculation.
I believe he is confusing a compressor with a 4 cycle engine, where the four cycle engine requires two crankshaft revolutions to complete the intake-compress-power-exhaust cycle, unlike a compressor which requires only one revolution for the intake-output cycle.
I don't know about what he's thinking, Pete, but you are correct. I called my local Quincy service center and talked to the service manager. Each piston compresses on each stroke.
He also gave me the actual specs for the Quincy Model 244:
This also computes, since I remember asking the Quincy guys back in the '90s if I were to replace the gas engine with an electric motor, what size, and they told me 7.5hp. Given Richard Kinch's rule of thumb (4 CFM / hp) these numbers make sense.
What *still* doesn't make sense to me is the free air displacement CFM. All I know about this compressor is:
2 cylinders bore: 4" stroke: 3-1/2" each cylinder compresses on each rev max rpm: 900
I'm figuring something like 45 cfm free air displacement at 900 rpm, and the actual CFM at 100 psi is more like 25.4 cfm. This would give an absurdly low volumetric efficiency of 62%.
Anyway, it's just a puzzle. Maybe someday I'll figure it out. In the meantime, like most Quincy pumps, the actual machine just keeps on running.
Probably the statement, "Each piston compresses on each stroke" means that: A stroke is fore and aft travel of the piston per revolution. Each piston sucks air in on 1/2 stroke and blows air out on the other 1/2 stroke. Therefore 900 half strokes of 2 pistons would be the free flowing CFM of the device. Grant's original math was correct except he multiplied volume by 2. 1/2 + 1/2 =1.
Bob Sw>> How do you make a crankshaft that only moves the piston up every other rev? >
I don't know about what he's thinking, Pete, but you are correct. I called my local Quincy service center and talked to the service manager. Each piston compresses on each stroke.
He also gave me the actual specs for the Quincy Model 244:
This also computes, since I remember asking the Quincy guys back in the '90s if I were to replace the gas engine with an electric motor, what size, and they told me 7.5hp. Given Richard Kinch's rule of thumb (4 CFM / hp) these numbers make sense.
What *still* doesn't make sense to me is the free air displacement CFM. All I know about this compressor is:
2 cylinders bore: 4" stroke: 3-1/2" each cylinder compresses on each rev max rpm: 900
I'm figuring something like 45 cfm free air displacement at 900 rpm, and the actual CFM at 100 psi is more like 25.4 cfm. This would give an absurdly low volumetric efficiency of 62%.
Anyway, it's just a puzzle. Maybe someday I'll figure it out. In the meantime, like most Quincy pumps, the actual machine just keeps on running.
It seems to me, Robert, that more correctly each piston sucks air in on 1/2 a revolution of the crank and blows air out on the other 1/2. But the piston travels the full stroke length each time, and of course has the same bore. And there are two cylinders.
((pi * (bore/2)^2 * stroke) / 1728) * rpm TIMES NUMBER OF CYLINDERS
i.e. total cyl vol. in cubic inches, converted to cubic feet, times rpm = cfm of the free air displacement variety
I wish I could understand how you figure a cylinder only pumps half its volume per crankshaft revolution. If that were true it would make mathemtical sense.
Grant
Robert Sw> Probably the statement, "Each piston compresses on each stroke" means that:
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