Flight Testing for Speed
The first step in developing speed mods is proper testing. By proper, I mean the tests have to be run in a way that provides repeatable results over a wide variety of conditions, since our quest for speed is a year-round pursuit.
To achieve this, we must eliminate all variables, so that the tests are run under exactly the same conditions each time. The same weight and c.g., identical power settings, running at the same density altitude, and consistent piloting are essential.
To eliminate winds aloft from our variables, I use the spreadsheet at the National Test Pilot School website. By flying 4 legs at approximately 90 degree different headings, and recording GPS groundspeed and ground track for each leg, the spreadsheet will calculate the average ground speed for 4 sets of three legs, and also give a standard deviation for the data set. The standard deviation is a measure of quality of your data, and should be below 0.5 for a good run. I will usually fly 3 or 4 sets (I call them "squares") during each test flight. I will fly 3 or 4 different days for each mod, and take an average of all (so 12 to 15 squares worth) to find a resultant speed for a particular mod. It is important to have a steady air mass, one with little vertical movement, and steady winds aloft over the test area.I always fill the tanks before the flight, and fly by myself. I use the Tru-Track autopilot to fly headings and hold altitude (this provides the added benefit of giving me time to watch for other traffic. If you have to hand fly the airplane, I strongly suggest a co-pilot to record data and help watch).
Power Setting
I always set the power at 2500 rpm, wide open throttle, 75 degrees rich of peak. The fuel flow will vary, because the power output will vary with the manifold pressure.
Density Altitude
By flying at the same weight (induced drag) and the same density altitude (parasitic or form drag), the total drag is kept constant. I fly at 11,000' density altitude, using the E6B function in my GPS to calculate the altitude to fly based on barometric pressure and outside air temperature. I try to fly in the middle of the barometer, that is, somewhere near 29.92 in Hg. If the barometer is very high (often 30.50 or so in the summer in this area) or very low, I get skewed results due to the rising or sinking of the overall air mass.
It is important to understand the distinction here between ambient air temperature, and total air temperature. Total air temperature is the temperature that your OAT gauge reads. It includes the "ram rise" or heating due to air friction. Ambient air temperature is the temperature of the air mass you are flying through. To find the ambient temperature, we must calculate the ram rise, and subtract that from the total air temp.
To simplify, in dry air the ram rise is about 0.2 times the mach number squared, times 288 degrees C. At 170 knots indicated, and at 11,000 ft d.a., it is about 5 dC.
Conveniently, the Garmin GPSs (and, I presume, other brands) include the ram rise calculation on the E6B page. You will see that when you enter the OAT, barometric pressure, and indicated altitude, you get a calculated density altitude. Then, when you enter the indicated (calibrated) airspeed, the density altitude drops by 500 ft. or so. This is because the unit has calculated the ram rise, subtracted it from the OAT you entered, and used the new value to calculate the density altitude.
It will still be important to record the total air temperature, so we can use it later in power calculations.
Adjusting for Power Output
Again, by flying at the same weight (induced drag) and the same density altitude (parasitic or form drag), the total drag is kept constant. This approach was chosen because it is hard to calculate exactly how the total drag varies with a change in density altitude.
The power output is not constant when changes in the OAT causes us to fly at different altitudes to achieve the same density altitude. This is because the manifold pressure is varying, even though the density is the same. It is well known that the airspeed varies with the cube root of the power change, so if we can calculate the power change, we can adjust our airspeed results, and eliminate another variable from our testing.
Since we are interested in a spreadsheet we can enter raw data into and get results, the charts in the Lycoming manual are no help. Richard Shelquist provides an excellent write-up at http://wahiduddin.net/calc/cf.htm and although he is referencing race cars and drag strips, it all still works.
The SAE provides the following formula (of course, I am making the assumption that all 4 stroke naturally aspirated engines will be subject to the same rules).
Here, cf is the correction factor (which we multiply by 100 to get % power), Tc is the total air temperature (the engine inlet sees the same ram rise as the OAT probe) in dC, and Pd is the dry air pressure in millibars (mb).
To find the dry air pressure, we must subtract the vapor pressure due to humidity from the total air pressure. We can read total air pressure by setting our altimeter to 29.92, and then converting the units to millibars.
p(h) = p0 (1-h/145457)^5.25635 millibars
(from John T. Lowry's pamphlet How the Atmosphere Works)
For our purposes, the easy way to do this is to use the dew point. Since the dew point is fairly steady throughout an air mass, we can use the reading we get from the ASOS at the nearest airport.
where Tc is the dew point in dC, c0 = 6.1078, c1 = 7.5, and c2 = 237.3
Now, the dry air pressure Pd = P(h) - Es. We can just substitute into the above equation for correction factor, and then apply the old cube law to the true airspeed from the NTPS spreadsheet to get a true airspeed that has been corrected for the day's atmosphere, relative to our standard density altitude.
TAS (corrected) = TAS (raw) * (cf (today)/cf (base))^1/3
For my own testing I chose a baseline density altitude of 11,000 ft. This is because I live in Colorado, and I need to go this high to avoid terrain in the winter time. If I lived in Ohio, I would choose 8500 ft as a baseline density altitude.
These equations are a bit intimidating, but once they are entered into a spreadsheet, we can just enter the data each time we fly, and get an average true air speed, corrected for the conditions on that day. This allows us to do our flight testing summer and winter, regardless of the atmospheric conditions, as long as we have a well behaved air mass.
Here is an Excel spreadsheet with all the equations entered. I am hoping it will be fairly self-explanatory. You can extend the file to more flights by copy/paste functions. I have taken the shortcut to make ram rise equal to 5 dC (close enough for the RVs, you may need to calculate it for your own airplane if you have a Lancair or something).
The data included on the above spreadsheet is made up. I chose the values to illustrate how things change as we go from a standard day to a very cold day, and a very warm day, and finally, a warm and humid day. You can see that a moderate humidity can raise the density altitude 250 feet, and make a real difference in the adjusted speed. This is much more critical in the summertime, because warm air can hold a lot more water vapor than cold air.
As you can read on other parts of this website, I have been doing this testing since I first flew the airplane. It has helped me state with confidence, for instance, that the MT prop was 4 kts slower than the old Hartzell, and that the new blended airfoil Hartzell was two knots faster yet. I have also used the test results to test various mods that I have tried. Some of these were well known to provide a speed increase, and some resulted from my own crackpot ideas.
Back to RV Home