Tailwind (Part II)

A while ago I posted a picture of my airspeed indicator and my GPS and asked you to calculate my tailwind. It's slightly harder than it looks, and you were missing a couple of pieces of information required for the complete calculation.

The airspeed indicator is showing 149 kts and the GPS 223 kts, so if you assume that the former is how fast the airplane is moving through the air and the latter is how fast the airplane is moving over the ground, it would seem completely reasonable to subtract them to determine how fast the air is moving over the ground. And that's how you arrived at your first collective guess of 74 kts.

The problem with that argument is that the airspeed indicator is calibrated to show true airspeed only at sea level and standard conditions. At higher altitudes or significantly non-standard temperatures, it needs to be adjusted to get the true airspeed, i.e. the speed the airplane would be going over the ground in zero wind. The true air speed increases with respect to the indicated airspeed by about two percent per thousand feet above sea level. I see from the GPS that I'm flying at about 9500' asl, so an in-the-head calculation has the true airspeed about 19% higher than the indicated, or 178 kts. That would suggest a tailwind of 223 minus 178, which equals 45 kts.

That is pretty rough, and assumes standard conditions. To get more precise than the two percent rule-of-thumb, you'd need to know the calibrated airspeed, the outside air temperature and the pressure altitude.

I didn't give you--and indeed didn't record--the outside air temperature but I think I had mentioned temperatures around freezing: raining some days and snowing others, and that a warm front was approaching, so you wouldn't be wrong to guess that after the arrival of that warm air mass there might be surface temperatures below standard but above freezing, around 5 to 10 degrees C. The temperature can be expected to drop off about 2 degrees per thousand feet of altitude, so at 9500' it might have been -5 to -10, and I recall -10 being about what I saw on the OAT gauge.

You know I was VFR on this trip: I think I mentioned the holes in the dashboard where some of my IFR instruments ought to be, and you see that the bearing is southeast. Therefore, according to what in Canada are still known as the cruising altitude orders I should have been at an indicated odd thousand foot altitude plus 500'. The GPS shows me at 9359', so that confirms that I was flying at an indicated 9500'. The difference between GPS altitude and indicated wouldn't be 2000' at these temperatures over prairie. (In very cold temperatures with mountain wave effect the GPS altitude could be 3000' lower than indicated). The difference between indicated altitude and pressure altitude depends on the altimeter setting, but I already sent my operational flight plan from that leg into company for filing, so I don't have the recorded altimeter setting to calculate from. We'll assume standard pressure, so that pressure altitude would be the same as indicated. It wasn't far off.

Calibrated airspeed corrects indicated airspeed for position error, but in cruise this difference is negligible, so I'll stick with 149 kts as the CAS.

I then use an E6B flight computer to crunch the numbers. I don't have one with me as I type, so I used a simulator from the web. Punch in 149 kts, -10C, and 9500' and I get 168 kts TAS. And 223 minus 168 equals 55 kts.

There's actually a calculator built right into this particular airspeed indicator, as someone pointed out, but the photograph is not clear enough to show it. (The reader who zoomed in and read the TAS there anyway may have seen it correctly, but I hadn't set that calculator, so its indications were meaningless). If I had used it, I would have set the pressure altitude opposite the outside air temperature at the top, then the needle that shows 149 kts on the main scale would also be pointing to a value on the white, outer scale, which would be the true airspeed. I'll try to get a better photograph of it sometime.

This is the reverse of the calculation one does to determine how long it will take to reach destination given a particular wind. But most of us cheat and use computer programs that do that for us now.