# Help needed with an autopilot formula, (vertical speed)

Discussion in 'General Math' started by Simon, Jan 24, 2009.

1. ### SimonGuest

Hi,

I am trying to come up with a formula that would help me with a simple
autopilot software I am writing.

I just want to concentrate on the rate of climb for now.

In my example I start my flight 'straight and level' with an elevator
setting of 0% and a climb rate of 0fpm.
If I change my elevator setting to 1% my climb rate will changes to 100fpm.

But the vertical speed does not change immediately, rather it changes to
1fpm, 2fpm and so on to eventually settle at 100fpm.

Is there a formula, using those differences, to calculate what the eventual
climb rate will be given those changes?

I was thinking of using the current vertical speed, the previous vertical
speed and the time difference between the two.
But I don't know if only one difference will give me the right target,
(final), value.

I suspect that the more time differences and vertical speed differences I
have the more accurate my final calculation will be.

Any suggestion/formula on how I could solve that problem?

Many thanks

Simon

Simon, Jan 24, 2009

2. ### hagmanGuest

Well, if you see a car starting e.g. at a traffic light, how
goo dcan you estimate the speed it will eventually accelerate to
from observing just the first few seconds?
Probably the model of the car has more influence on this than
the first observed speed differences....

hagman, Jan 24, 2009

3. ### Greg NeillGuest

You might try an exponential function of time, if you're looking
at creating a smooth transition to the final value. Something like:

v(t) = v0 + (vf - v0)*(1 - e^(t/T))

v0 = initial vertical velocity
vf = final, or "target" vertical velocity
T = time constant for the manoeuvre
t = time since the beginning of the manoeuvre

So the (vf - vf) term sets the total velocity change that will
take place over the time of the manoeuver, and the (1 - e^(t/T))
term gives the change its shape over the total time time.

You can give T a value that is 1/5 the total manoeuvre time. That
is, if you think that the plane will reach its final vertical
speed after 20 seconds, set T to about 4. The rule of thumb for
these time constants is that essentially all the "action" is about
done after five time constants.

If your model is a simulation that is progressing in time steps
you'll have to keep track of the time from the beginning of the
manoeuvre to use as the value of t.

Greg Neill, Jan 24, 2009