Rainboe,
Don't over-simplify... the increase in alpha is not the same as the cosine(climbangle). But your basic intuition of decreasing alpha with climb angle is right (except possibly for something with L/D less than one.... I'll have to look into that....)..
To all,
OK, promises, promises...
Here's my scribble.
Not quite so artistic, so let me explain.
What we are looking at, are the horizontal and vertical force balance (steady state, remember?).
I've been looking at the other extreme from Rainboe's example, i.e., the typical climb rather than the vertical climb.
With a climb at 6° (my earlier example) or even 15° (cos = 0.97, quoted by Rainboe)...
Horizontally:
- the drag component barely changes,
- thrust changes a lot, because suddenly the thrust has to "drag" L*sin(ac), the horizontal component of L, "upstairs".
Vertically:
- the weight doesn't change,
- the drag component is now tilted downward,
- the thrust component is tilted upwards, and thrust is now larger than the drag, so the net result is an upwards force.
To get back to a steady state, we'll have to reduce L*cos(ac).
After plugging in the rest the maths... that comes down to reducing L, hence the AoA.
So, conclusions?
- At the typical climb angles of most aircraft, be them Cessna or Airbus, you will barely notice the change in angle of attack (it's all cosine something, and the cosine is almost 1 (one) ).
- You will certainly notice the difference in thrust (or engine power - which is the same in this context) to maintain a steady climb under the same conditions as in horizontal flight.
- If you're a fighter jock with more puff behind you than your aeroplane weighs... have a go at all means to try the other extreme of our discussion. But remember what we said. You may need to pitch down a bit for that perfect vertical climb.
CJ