Understanding Relative Air Density
I have always said that understanding carburetors makes it easier to understand fuel injection (and understanding fuel injection makes it easier to understand carburetors). Back in 2004, I designed and built a small batch of electronic RAD gauges for friends, fellow tuners and racers. I called it eRAD. A few even ended up outside the US so I provided an option to display metric units, but RAD itself is dimensionless. I wrote the following to supplement the eRAD user manual. You may find it interesting if for no other reason than to gain an appreciation of what the OSSA ECU is doing to make your life easier.
Once your bike is set up and running perfectly, your ongoing challenge is to keep it that way. A relative air density (RAD) gauge may provide the information you need to alter the jetting for different atmospheric conditions.
RAD increases with an increase in barometric pressure (e.g., going to a lower elevation) and/or a decrease in ambient temperature. Conversely, RAD decreases with a decrease in barometric pressure and/or an increase in temperature. As far as RAD is concerned, standard temperature and pressure (STP) is defined as a temperature of 59 degrees F with a barometric pressure of 29.92 inches of mercury. STP is one point at which 100 percent RAD exists. Although bike tuners typically deal with RADs that are less than 100 percent, a RAD of greater than 100 is possible. (Operating in a cold environment, snowmobile tuners regularly work with RAD numbers greater than 100.)
If your bike is jetted spot-on at a RAD of 100 and makes 100 horsepower, it could make 110 horsepower at a RAD of 110 with the proper jetting. Similarly, at a RAD of 90, the best you can hope for is 90 horsepower.
Making horsepower is all about providing the appropriate amount of fuel for the amount of combustion air available under the prevailing atmospheric conditions. Neglecting delivery ratio, each time a piston descends it pulls in the same volume of air, but the mass of that volume of air varies with temperature, barometric pressure (elevation,) and humidity. Chemically speaking, it is the mass of the air (oxygen portion) that determines the mass of fuel needed for optimum combustion efficiency (horsepower production).
Your job as a tuner is to jet the bike for the air density you encounter from track to track and day to day (and sometimes even from hour to hour). Typically, tuners using a RAD gauge will produce a copious notebook (developed by trial and error) detailing the proper jetting for a given RAD.
Why trial and error? Firstly, a given change in RAD does not dictate a directly proportional change in jetting. (For example, a 5-percent change in RAD does not equate to exactly a 5-percent change in jet size.) Secondly, identical RAD numbers can be achieved under vastly different atmospheric conditions. The same RAD number can be seen in a location with a higher temperature and higher barometric pressure as in one with a lower temperature and lower barometric pressure. For example, when it is 100 degrees F at Willow Springs (elevation of 2600 feet) the RAD will be about 84.5. At Pikes Peak (elevation of 5400 feet) the same RAD would occur at a temperature of 45 degrees F. Although the RAD numbers are the same, theoretical optimal jetting would be one size different for a nominal 350 main jet. You'll see why shortly.
A simple mechanical RAD gauge can yield accurate results under the proper conditions. “Proper conditions” are low or constant humidity and, additionally, the elevation must be constant or the temperature must be constant. Although changes in barometric pressure due to weather are taken into account by a RAD gauge, their effects are usually minimal – a much greater factor is a significant change in elevation.
Most of the time, you can achieve satisfactory results with a mechanical RAD gauge and copious notes. But a mechanical RAD gauge is not the panacea it is made out to be because it only gives a “bottom line” number without allowing you to see the individual contributions of the two factors – temperature and barometric pressure – that comprise that number.
The best way to jet a bike is to treat separately the two or three factors that influence RAD. Why two or three? Humidity sometimes enters the picture. When it is considered, we call the resulting value “corrected” RAD.
Because mechanical RAD gauges do not take humidity into consideration, many racers use spreadsheets or tables to account for it. In some parts of the country, humidity is a negligible factor. However, in large parts of the U.S., humidity is a factor. For example, at Brainerd, 90 degrees F with 90% humidity is not unheard-of. Under these conditions, almost 5% of the available “air” is displaced by water vapor. This results in a corrected RAD which is 4 smaller than the uncorrected value (as would be displayed by a mechanical RAD gauge).
Jetting must change in direct proportion to absolute temperature. A 10 percent change in absolute temperature necessitates a 10 percent change in jet size. Absolute temperature is a scale referenced to “absolute zero” rather than to the temperature of freezing water. To convert Fahrenheit into absolute temperature, add 460. This is called the Rankine scale. For example, the difference in absolute temperate between 70 degrees F and 90 degrees F is not quite 4 percent (90+460) / (70+460) = 1.038.
Jetting does not change in direct proportion to barometric pressure. A 10 percent change in barometric pressure necessitates only a 7.7 percent change in jet size. This is because a change in barometric pressure also affects the pressure exerted on the fuel in the float bowl. Therefore, a change in barometric pressure will automatically alter the fuel-air ratio somewhat. How do you go about achieving an X-percent change in jetting? Fortunately, the number stamped on Mikuni hex-head jets represents a nominal flow in cc per minute at a particular test pressure. Therefore an X-percent change in jetting is just an X-percent change in jet number. For example, a 360 jet is about 3 percent richer than a 350 jet.
As a side note, round-head Mikuni jets are not as simple to use because their numbering scheme is based on aperture size instead of flow rate. Because flow is proportional to area, it takes an extra step to convert aperture diameter into area. The formula is: area = pi x radius x radius. For example, a 107.5 jet has a nominal diameter of 1.075mm. The area of this jet is about 0.91 square millimeters. A 3 percent richer jet would be a 109 (which does not exist, so a 110 would have to be used).
Incidentally, the barometric pressure reported on a TV weather forecast is not the actual barometric pressure – unless you happen to be at sea level. Reported barometric pressure is always corrected back to the pressure it would be if you were at sea level. Thus in Denver, for example, when the barometric pressure is reported to be 29.6, the actual air pressure is more like 24.6 (You can figure about 1 inch of mercury for each 1000-foot change in elevation, but the table below is exact).