An aircraft's climb rate is basically determined by how much power is left over, after fighting drag, that can fight gravity. Climb speeds (as most other performance speeds) are usually given in calibrated airspeed (CAS), which is indicated airspeed corrected for the errors of the instrument and the pitot/static system. After all, the wings and prop, as well as the engine, all behave in relation to a specific air density. So for our purposes we'll talk about indicated airspeed (IAS), which is the speed indication generated by ram air pressure into the pitot tube. Obviously, reduced air density at a given actual speed through the air (TAS, or true airspeed) gives a lower reading on the airspeed indicator.
Engine power (unless it's a turbocharged engine) also decreases with reduced air density. This reduced air density can be caused by higher altitudes, higher temperatures, or both. Because this is so highly variable, we typically relate aircraft performance to a "standard atmosphere" which is sea level with 29.92" on the barometer (or 1013 millibars, for metric users) and 59� F (or 15� C) and zero percent relative humidity. And we figure a 3.5� F (2� C) drop in temperature for each 1000 feet of altitude increase. This is how performance figures for aircraft are presented in the manuals, also.
Given the above, an aircraft responds in a certain way related to air density, not altitude, so at a given weight it will stall at the same indicated airspeed, regardless of the actual (true) airspeed, temperature, altitude, etc.
So Vy the best rate of climb airspeed, meaning that it is the best combination of engine power and drag (remember drag quadruples as the airspeed doubles) that leaves you with the most engine power remaining with which to climb. So long as you have the same amount of engine power available, this indicated airspeed for Vy will remain the same regardless of altitude/air density, which we call density altitude, meaning we correct altitude indications for pressure and temperature.
But in a normally aspirated (non turbocharged) aircraft, power is reduced as density altitude increases. So there will be a gradual reduction in the indicated airspeed for Vy as you climb (remember, you have less power to overcome drag, and drag changes with the square of the airspeed), so a slightly slower speed reduces drag but reduced power gives you a slower rate of climb.
Now about best angle of climb airspeed. This angle can also be viewed as how much altitude is gained per foot/mile/etc. of forward travel. Obviously, at a slower airspeed you cover less ground, so at the same vertical rate the angle would steepen. But we've already shown that there is only one speed at which you get the max rate of climb. However, recall that squared relationship between speed and drag -- it also works in reverse, so that drag decreases with the square of the speed reduction.
This means that at a slightly slower speed than Vy, the angle becomes a little steeper. So the manufacturers test and calculate until they find the optimum relationship between speed reduction and drag reduction that results in the airspeed that gives you the best (steepest) angle of climb (Vx), which is good for clearing obstacles. Just as Vy decreases with altitude, Vx increases with altitude.
As density altitude increases, remember, the engine power decreases, so these two values (Vy and Vx) slowly converge as you climb until they are the same at the absolute altitude of the aircraft, and Vy is the only speed which allows you to maintain altitude -- you can't actually climb from that point.
In a turbocharged aircraft, the two values will remain essentially the same up to what we call the "critical altitude," that is, the altitude above which the turbocharger no longer maintains sea level power, above which point the two values behave much as they do in a normally aspirated aircraft.
Last edited by Pace; 27th Feb 2014 at 07:46.