How Fast Are You Really Going?
Maybe not as fast as you think
By Paul Lipps, email@example.com
Here I am toolin’ along in my Fast-Glaster behind that big ol’ TIO-540, lookin’ at those two multi-function displays (MFD). 280 knots! 322 mph! Hot dog - and I just came from the avionics shop where the avionics tech worked his magic on my pitot-static system while I fed numbers into the computer from my laptop, so I know what it says is true.
Man! Could anything be better than this? After I get back on the ground my “master-of-skepticism” techie buddy gives me that raised-eyebrow look when I lay the numbers on him. “What’s wrong? Why are you giving me that fishy look?” I asked. “I just got this thing calibrated to the nth degree, so don’t go givin’ me that ‘sumthin’s wrong here’ look. C’mon. Jump in and I’ll show you!”
We zip on up to 7,500 feet and level off. He asks me to slow to 90 knots indicated. After a while of staring at the panel, he makes a note and tells me “to give it all she’s got.” He then asks me to put it on autopilot and altitude hold, and then twirl the heading knob to keep us in a continuous turn. He makes more notes, then after a little more than one turn, he tells me to take up a certain heading. I pointed with unconcealed glee as the true airspeed (TAS) numbers on the MFD slowly climb to 279 knots! A few minutes and many scribbled notes later, he had me turn 180 degrees. More minutes and notes and he said to land.
He then got on his cell phone, and I heard him give my plane’s registration number and then ask for surface barometer setting and forecast temperature and winds at 7,500 feet in our area. He wrote those down, looked at his notes, entered some numbers on his circa 1979 HP-41C programmable, scientific calculator, pushed the buttons, and then said, “You’re not going to like what I tell you.
“The first thing I had you do, slowing to 90 knots indicated airspeed (IAS), was so I could see what your outside air temperature (OAT) was at that speed; it came within 1 degree of forecast. That’s good! When we flew in a circle, with your autopilot keeping altitude constant, I watched your groundspeed and track on the GPS display, and noted the track associated with the highest and lowest speeds. That gave me the wind direction and speed. Next I had you fly with the wind until groundspeed stabilized, then against the wind. During those two runs I wrote down IAS, groundspeed, altitude, density altitude, OAT, true airspeed, and fuel flow. Averaging the groundspeeds from the runs in both directions gave me your true airspeed.”
“So tell me, what was it?” I asked.
“First, let me tell you what I found,” he replied. “As we went from 90 knots to your top speed, your OAT increased from 17ºC to 25ºC, a total of 8ºC. This is what is called stagnation temperature rise. It is due to the impact, not friction, of the air molecules striking anything in their path, such as your temperature sensor. It is the same thing that heats up SR-71s and burns up meteors and shuttles! This temperature error caused your computer to think your density altitude was 10,320 feet rather than 9,410 feet, a 910-foot error, which caused it to give a +1.4 percent error in calculating your TAS. However, the location of your static ports appears to be where the actual pressure is 0.1 inch less than true static pressure. As a result, your indicated airspeed is 4.5 knots high at 238.5 knots, rather than 234 knots.”
“All of that is great, but will you please tell me, what do you think my true airspeed is?” I asked.
“I won’t keep you in the dark any longer!” he said. “Your true airspeed is 270 knots, 311 mph, which is still spectacular, although a full 10 knots lower than you thought!”
“What can I do to fix this?” I asked.
“First, we need to move your temperature sensor into some shielded, stagnant location where it is out of the direct flow of air and the engine and cooling exhaust,” he said. “I have two sensors in my plane, one behind the rear spar and ahead of the flap, and the other inside, above, and in back of the elevator spar clearance-hole in the fuselage tail cone. They usually agree within 1°C and show no rise with increasing airspeed. Next, we’ll put two or three layers of cellophane tape just behind the static ports. That will increase the pressure slightly. We only need 0.1 inch. Then we’ll go test these mods the same way we did on this flight.”
So now I have true airspeed. Actually, I liked what I had better! But I’ll tell you this; when I go to sell the plane, guess what happens to the tape and temperature sensor?
Stagnation Temperature Rise:
Ts-TA = TA(k-1)(M)²/2 where:
Ts, stagnation temperature, °R;
TA, actual temperature, °R;
°R = °F + 459.7°
k = specific heat ratio of air = 1.405;
M = Vs/V;
VS = 49.04(°R)^½, feet/second
V = true airspeed, TAS, appropriate units
TR = temperature rise, °F
Since VS is a function of TA, the formula can be reduced and TA eliminated, leaving only the temperature difference, which gives TR = (TAS)²/c. This gives “c” as: