Air compressors for the home or small shop have been advertised and sold with ridiculously inflated horsepower ratings. This was especially true before the year 2004, when the US government said it would enforce more honest ratings (see the end of this essay), and it seems to be returning to the marketplace after a year or two of spotty compliance. The specs and stickers on the unit likely do not tell the truth, and add confusion instead of critical information to buying decisions. But you do not need a testing laboratory to calculate true horsepower or CFM delivered. I will explain below how to estimate these ratings from pressure readings and elapsed time measurements.
The way to measure true power is to measure the time it takes to pump the reservoir tank of known volume from a known starting pressure to a known ending pressure. Then you can figure the true CFM from the difference in starting and final pressures, times the volume of the tank, divided by the time it took to pump up. You can also time the pump-up cycle from the cut-in to the cut-out pressure, since that's how one usually runs a compressor. These true performance measurements are impossible to fake.
My Chinese-import compressor bears a big yellow sticker claiming the unit delivers 6.5 HP, and 10 CFM at 90 psi. Let's see what it really delivers.
My compressor says it has a 25 gallon tank, and I confirmed that with some rough measurements and volume calculations. If I trigger a refill cycle by bleeding out air slowly with the relief valve, I observe on the tank gauge (not the downstream gauge) that the compressor "cuts in" at 85 psig and "cuts out" again at 102 psig, a difference of 17 psi. It cranks for 35 seconds to build up that pressure.
Divide the tank volume in gallons by 7.48 (1 cu-ft = 7.48 gallons) to get the tank volume in cubic feet. Thus the tank volume is 25 gallons / 7.48 gal/cu-ft = 3.34 cubic feet.
In units of atmospheres of pressure, since 1 atm = 14.7 psi, the 17 psi of pressure added during the cycle is 17/14.7 = 1.16 atm of pressure during the cycle.
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) per minute. (Note: A CFM does not mean in any sense the compressed volume.) So the unit really measures the mass of air flowing per minute, not volume per minute, since a cubic foot of free air is a unit of mass. Some people labor under a stubborn misundertanding that these units refer to the flow of compressed volume (as opposed to free air volume), but this is flatly wrong.
Thus in one cycle, the rate at which air is being pumped into my tank, is the pressure rise times the volume of the tank, or 3.34 cubic feet * 1.16 atm = 3.87 cubic feet per 35 seconds. To proportion the 35 seconds up to minutes, to get the pumped volume per minute, multiply by 60/35, or 3.87 * 60/35 = 6.6 CFM (at 85 psig).
The error range in our estimate is perhaps about 30 percent (the true value might perhaps be as much as 8 CFM or as little as 5 CFM). Certainly this is not performing at 6.5 HP like the advertising sticker says, or the 10 CFM on the data plate. I was hoping for better, especially since it is wired for 240 VAC.
Now you know why the data plates on the electric motors have blank boxes for horespower ratings. A true power rating from the motor manufacturer would expose the lie of the advertised compressor power.
Tip: Any motorized device that takes power from a 120 VAC outlet, surely delivers less than about 2 HP, and likely far less. Why? Standard AC cords are limited to 15 amps of current, or about 1800 watts. At 746 watts/horsepower, and considering efficiency losses, 2 HP is all you can get, and even then the starting currents might be tripping circuit breakers.
Tip: CFM ratings are meaningless without an associated delivery pressure. I have a 600 CFM compressor in my garage that uses only 1/3 HP! (It's a fan delivering 0.1 psi.)
Rules of thumb:
Assumptions: We have assumed a single-stage compressor, which is to say, just about anything small or portable; two- and three-stage compressors are somewhat more efficient, and will yield better results, but only become economical in larger sizes. Our proportioning calculations are based on the ideal gas law PV = nRT with isothermal compression (pressure and volume of the compressed air are changed, but the temperature is not, which is the case for cooled compressed air). This method does not account for ambient humidity condensing in the tank, for different ambient pressures, or for heating/cooling of the air; these are relatively minor but not necessarily insignificant factors.
Reference: Machinery's Handbook (26th edition, see http://www.industrialpress.com/mh.htm) has an excellent section on analyzing compressed-air systems, including formulas and tables on the horsepower required to compress air, and losses in pipes and hoses. Marks' Standard Handbook for Mechanical Engineers describes the thermodynamics of expansion and compression of air in the section on "General Principles of Thermodynamics", subsection "Special Changes of State for Ideal Gases", item 5 "Polytropic"; and practical compressor technology in the "Pumps and Compressors" chapter.
Other Terms: An "SCFM" (standard cubic foot per minute) is a CFM produced with input air at 68 deg F, 36 percent RH, and 14.7 psia pressure (the mere letters "SCFM" refer to no official standard, and while various temperature and RH values are in use, these are the most commonly accepted values). "Displacment CFM" is the rate of volume displaced by a reciprocating piston compressor, which is compared to the delivered CFM to evaluate volumetric efficiency. "Peak horsepower" typically means the electrical power drawn by the motor at the instant of starting; this figure is a meaningless specification because it says next to nothing about the sustainable horsepower delivered by the system. "Peak horsepower" most definitely does not mean anything like "what you get if you run this unit full throttle", "what the motor can deliver for short periods of time", or "what the motor can do if heavily loaded". Also, rated CFM at "90 psi" can really mean the inflated value measured from the CFM input during a pump-up from 0 to 90 psi. Such trickery is what you get in the absence of well-defined engineering testing standards and methods, which is to say, "consumer" mentality. This applies to larger systems like the 5 HP 80-gallon units common in auto repair shops, just as well as the homeowner models.
Wet Air: As much as you might want to believe that your carefully-chosen compressor is providing a useful supply of compressed air power, the fact is that without an expensive drying unit, your compressed air is of very limited application. This is because the "air" being sucked into your compressor does not consist of just compressible gases like nitrogen and oxygen, but lots of water vapor. In all but the very driest climates, the compression from atmospheric pressure (14.7 psia at sea level) to the total tank pressure (typically, 100 psig = 115 psia, or so) compresses the atmospheric water vapor to the condensation point inside the compressed air tank and delivery system. This is why you have liquid water collecting in the tank, which must be periodically drained. But the water does not stop at the tank. While you can strip any liquid water out of the air line with an inexpensive coalescing filter, the water vapor remains everywhere in the flow of compressed air at close to the condensation point (100 percent "relative" humidity), and will condense into liquid with the slightest cooling downline from the initial heated temperature. This is why you can have liquid water sputtering from your air lines into your tools, tires, paint spray, etc., even after a so-called filter/dryer; hot, steamy air fills the air line even after the filter, and if allowed time to cool, the humidity condenses into liquid water. While this water-contaminated air spoils the lubrication in your air-powered tools, robs power, throws your tires off balance, etc., it positively ruins the operation of tasks like painting and sandblasting that cannot contaminate the work with specks of liquid water or water vapor. You do not just have compressed air, you literally have compressed steam as well. (Tell your friends your shop is steam-powered!)
Dry Air: The only solution to wet air is a refrigerated air dryer. This is a unit that costs more than many small compressors. It is essentially a small air conditioner that chills the air stream running through a coiled tube, thereby condensing almost all the water vapor to liquid, which liquid is then separated and drained out of the unit. Such a unit is all that is needed for most dry air applications, yielding a relative humidity of about 10 percent in the output air, literally drier than a desert. For demanding applications requiring even less humidity, dessicant filters with a complex system to regenerate themselves with heat are used, typically after a refrigerated dryer, yielding a truly near-zero humidity. The grim thermodynamic reality is that there is no easy or cheap way on a small scale to purify air from contaminating water vapor. Water is a problematic contaminant in compressed air, and wet air is greatly inferior to dried air. Think of it as another thing the Sears salesman didn't tell you about the compressor's performance, namely, that without further expensive treatment, it produces water-contaminated output.
Caveats: Making estimates with the pump-up timing method requires trustworthy measurements. Pressure gauges are often way off calibration. Confirm the specified tank volume by measuring the geometry instead of just accepting the specified value (watch out for imported units that have had design changes without updated documentation). Measure the elapsed time carefully over several cycles. Measuring delivered air power also requires that you consider the resistance and losses involved in the regulator(s) and hose(s) between the tool and the compressor; these can rob significant amounts of power.
The Manufacturers Repent (or Did They?): In early 2004, consumers and the government, organized under a class-action lawsuit, attempted to force several major manufacturers of air compressors to stop advertising inflated values for compressor horsepower. The lawsuit alleged that "the companies knowingly labeled, promoted and sold consumer air compressors with electric motors as having higher horsepower motors than they actually contained." The settlement requires manufacturers to measure horsepower based on the continuous power output of the electric motor shaft, or continuous power input to the compressor shaft. Advertising based on "peak power", "max developed power", "max kinetic power", or "breakdown torque", is no longer to be used. Manufacturers agreeing to this settlement include Campbell Hausfeld, DeVilbiss, Ingersoll-Rand Co., and Coleman Powermate, Inc. While the usual boilerplate in the court settlement absolves them of any illegal actions, these firms implicitly admit that their behavior was deceptive and uneconomic. See http://www.aircompressorsettlement.com/ [broken link now, I guess they gave up on this]. Historical information on this settlement has been available at classactionworld.com.
In the years since this settlement, however, one sees just as much advertising and labeling of inflated compressor power as ever. The awards to consumers from the class-action lawsuit consisted of nothing more than discounts for more mislabeled equipment from the deceptive advertisers!
Let us be generous and think of the whole affair this way: perhaps none of those manufacturers wanted to be inflating horsepower ratings, but once specifications started being inflated (however it started), they all had to do so as a matter of marketing self-defense. It took a consumer lawsuit to get them to all agree to return to the most elementary rules of honesty and fairness. The horsepower output of a machine is as certain and standardized as the weight of a bag of apples at the produce stand. Honest weights and measures are as important to prosperity of the air compressor business as any other.
Links: See Kevin Brady's essay The Numbers Game: A Primer on Electric Motor Horsepower Ratings, [5-page, 229 KB PDF file] which performs a similar critical analysis on electric motors in general.