Finding Vx and Vy

[Adrian N]

I am the lucky owner of a 1963 Jodel D140. It has a rather thin POH, with very little information about climb performance. The POH data is based on an aircraft equipped with a 62 inch pitch propellor. I actually have a newly overhauled 58 inch prop, and would be interested to know Vx and Vy at different weights and altitudes. Weight can vary from about 730kg with just me and low fuel, up to 1200kg MTOW. I fly quite a lot in the mountains, at altitudes up to about 12000ft, where flying at Vx can help one to cross ridges without spending a long time circling.

I imagine that finding Vy is a fairly simple matter of trial and error on a calm day. I don't know how one finds Vx. Can anyone suggest how I should go about this? Also, is it possible to determine Vx and Vy mathematically for different altitudes from one set of measurements, or does one need to repeat the tests?

I don't really need to know - the aeroplane has quite adequate performance and I don't envisage being in a situation where it is essential to fly precisely at Vx or Vy. But I would be interested, and it might give me a purpose (= an excuse!) to enjoy some flying.

Thanks in advance!

[Genghis the Engineer]

If you were closer, I'd offer to fly the tests with you for the fun of it - surprisingly I've never flown a Jodel.

The way I'd probably tackle this were I you, is to allow myself 3 trips, at three different weights - the lightest you can manage, MAUW, and somewhere about halfway between.

On each one (and having reasonably carefully calculated weight), you want to set up for a series of sawtooth climbs. So, let's say we'll do our tests between 4000 and 5000 ft (specific heights don't matter, only that you have still air and stick to the same heights), pick a speed initially reasonably below where you think that either Vx or Vy is likely to be, and establish yourself around 3,500ft. Then establish a full power climb, at that speed so that you should be stable on conditions as you climb through 4000ft - which is the point you start your stopwatch.

At 4,500ft (still in a steady climb) note what the VSI says.

At 5,000ft, (still in a steady climb) stop the stopwatch,

Note the time it took to climb through 1000ft, then come back down to 3,500ft again, and repeat this at (say) 5 knots faster. Keep repeating this until you are convinced that you're above either Vx or Vy, then go home.


Write all this down in a table, add a few extra columns, and work out your rate of climb from the time to climb 1000ft. Plot a graph of RoC versus IAS, and you'll easily see Vy (as well as how accurate your VSI was!)

Slightly more difficult now, add a few more columns. Firstly use the correction chart in your POH to convert IAS into CAS, and then make a density altitude correction to convert this into TAS. Next re-write both the rate of climb and the TAS in the same units (doesn't matter what units, but I usually use metres per second). Now from these values, work out the climb angle (which will be arcsin [RoC/TAS]).

From all of this, you can now plot a graph of IAS against climb angle - from that again the best climb angle will be obvious (don't be too surprised if it's worryingly close to the stall, when I've hit this, I generally declare an arbritrary Vx of 1.3Vs to give a sensible margin of safety above the stall).


So, you've now got Vx and Vy at this weight. Now, re-do this at the other two weights.

Plot another graph (you get through a lot of graphpaper on this sort of task - or you can do it in something like MS Excel) showing weight on one axis, and the Vx and Vy values on the other - that'll show you the relationship between speeds and weights - although neither speed is likely to vary that much with weight.



Now, if you want total climb performance, whenever you have a nice calm day and were flying anyhow, try and plan in a steady climb at Vy, up to whatever is your normal maximimum altitude, record time every 500ft or so all the way up, then plot a graph of time against density altitude - that'll give you standardised time to height. If you want to convert that into rate of climb, you need to do a bit of number crunching and calculate the derivative of height with respect to time. [My cheats way to do this is plot the curve in Excel, fit a trinomial curve to it, then manually differentiate that curve-fit with respect to time, and re-plot that.] Do this for a series of weights, and you've got a nice chart of climb performance with weight.

(Yes, you can do it all with maths, but you'd still need to do some testing to get the basic numbers to start with, some of the maths can be a bit approximate, and frankly this way is much more fun).



A few short warnings about safety. Keep an eye on engine temperatures - either from shock cooling coming back down in the middle of the sawtooth climbs, or from overheating during the continuous climbs. Always remember that when you're sat there writing numbers down, it's very easy to forget about proper lookout - so get that right (ideally, take somebody else and use them as a second pair of eyes).

Hope that helps,

G

[Adrian N]

Many thanks Genghis!

I'll probably wait until the summer heat has passed, in the interest of engine cooling, but I will try to follow your guidance. I will need to fit a rudimentary OAT probe to find density altitude, and would probably start climb tests with a high airspeed and decrease in 5 kt increments. I don't have a CHT gauge, and don't want to climb more than I need to at very low airspeed.

The flight manual gives an ASI position error correction to give Equivalent Airspeed, which I assume is the same as CAS?

As for the calculus, if I had been told as a child that it had a practical application to flying, I might have paid more attention in class! I'll tackle that one when I get to it.

Adrian.

[Genghis the Engineer]

Yes, for the speeds and altitudes you'll fly the Jodel, you can assume that EAS=CAS (there'll be a difference, maybe a few hundredths of a knot, so you can ignore it).

Yes, I don't think my schoolteachers ever actually told me that calculus was actually useful either. I suspect that they didn't know themselves.

G

[Shawn Coyle]

regarding OAT - may I suggest that you get a cheap digital OAT system from your local electronics shop - (KMart and Walmart in the US have them as well). For about $10 you get 0.1°C accuracy which will help tremendously in getting accurate data.
Get one with an 'outside' probe, and then tape the probe outside where it's not influenced by exhaust, etc, and keep the readout in the cockpit.

[Mork]

Correct me if I´m worng, plz. Instead of all of this, wouldn´t it be easier to fly a speed of approximately 1.3 Vsr. That would give you an approximate Vy.