Dyno Correction Factor and Relative Horsepower
 

So what's all this correction factor stuff anyway??

The horsepower and torque available from a normally aspirated internal combustion engine are dependent upon the density of the air... higher density means more oxygen molecules and more power... lower density means less oxygen and less power.

The relative horsepower, and the dyno correction factor, allow mathematical calculation of the affects of air density on the wide-open-throttle horsepower and torque. The dyno correction factor  is simply the mathematical reciprocal of the relative horsepower value.

What's it good for?

One common use of the dyno correction factor is to standardize the horsepower and torque readings, so that the effects of the ambient temperature and pressure are removed from the readings. By using the dyno correction factor, power and torque readings can be directly compared to the readings taken on some other day, or even taken at some other altitude.

That is, the corrected readings are the same as the result that you would get by taking the car (or engine) to a certain temperature controlled, humidity controlled,  pressure controlled dyno shop where they measure "standard" power, based on the carefully controlled temperature, humidity  and pressure.

If you take your car to the dyno on a cold day at low altitude, it will make a lot of power. And if you take exactly the same car back to the same dyno on a hot day, it will make less power. But if you take the exact same car to the "standard" dyno (where the temperature, humidity and pressure are all carefully controlled) on those different days, it will always make exactly the same power.

Sometimes you may want to know how much power you are really making on that specific day due to the temperature, humidity and pressure on that day;  in that case,  you should look at the uncorrected power readings.

But when you want to see how much more power you have solely due to the new headers, or the new cam, then you will find that the corrected power is more useful, since it removes the effects of the temperature, humidity and atmospheric pressure and just shows you how much more (or less) power you have than in your previous tests.

There is no "right" answer... it's simply a matter of how you want to use the information.

If you want to know whether you are going to burn up the gearbox with too much power on a cool, humid day, then go to the dyno and look at uncorrected power to see how exactly much power you have under these conditions.

But if you want to compare the effects due to modifications, or you want to compare several different cars at different times, then the corrected readings of the "standard" dyno will be more useful.

How's it calculated?

The Society of Automotive Engineers (SAE) has created a standard method for correcting horsepower and torque readings so that they will seem as if the readings had all been taken at the same "standard" test cell where the air pressure, humidity and air temperature are held constant.

The equation for the dyno correction factor given in SAE J1349 JUN90, converted to pressure in mb, is:
 

                         where:   cf = the dyno correction factor
                                     Pd = the pressure of the dry air, mb
                                     Tc = ambient temperature, deg C

The pressure of the dry air Pd, is found by subtracting the vapor pressure Pv from the actual air pressure. The relative horsepower is simply the mathematical reciprocal of the correction factor.

 Horsepower and Torque:

Power is the rate at which work is done. When the engine torque is turning the crankshaft and power is being delivered, the resulting horsepower may be expressed as:

which can be simplified as

                where:  hp = horsepower, hp
                            t = torque, ft-lbs
                            rpm = engine speed, revolutions per minute
 

This is a great formula. Basically it says that if you can keep the same amount of torque, then the more rpm you can turn, the more horsepower you get!

That's why Formula One and CART and IRL engines all turn incredible rpm. The faster the engine turns, the more power it can make (when it's properly tuned to operate at that speed).

Consider for example: a normally aspirated internal combustion engine typically produces about 1 to 1.5 ft-lbs of torque per cubic inch when it is properly tuned to operate at any specific rpm. With a 2 litre (1 litre is about 61 cubic inches) engine, producing 1.5 ft-lbs of torque per cubic inch, you would expect to get about 180 hp at 5200 rpm... but you will get a whopping 415 hp if you can get it to run at 12,000 rpm.

The 3.5 liter IRL engine is reported to produce about 650 hp at 10,700 rpm. That would be about 1.5 ft-lbs per cubic inch.

The Ferrari 3.0 liter Formula One engine is rumored to produce about 860 hp at 18,500 rpm. That would be about 1.33 ft-lbs per cubic inch.

And at the other end of the rpm spectrum, one model of the 360 cubic inch four cylinder Lycoming IO-360 aircraft engine produces 180 hp at 2700 rpm, which is 0.97 ft-lbs per cubic inch.

In general, production automobile engines that have a broad torque band will produce about 0.9 to 1.1 ft-lbs per cubic inch. Highly tuned production engines, such as the Honda S2000 or the Ferrari F50 are in the range of 1.1 to 1.3 ft-lbs per cubic inch. Highly tuned race engines such as NASCAR, IRL and Formula One are often in the range of 1.3 to 1.5 ft-lbs per cubic inch.