FF8s exponential
Here I estimate the behaviour of the exponential of the Futaba Field Force 8 super
transmitter. What we are looking for is the relation between the amount of stick
movement and the amount of servo travel.
I could not find the formula in the Futaba documentation, nor on the web.
There is a formula here
stating that it is P(e(Ap - A) / K).
But this doesn't really help, as they dont provide P, nor indicate what A, p and K are.
So we decided to make our own formula and estimations, properly fitting the actual behaviour.
Following the name 'exponential', f(x)=ep x must be the starting point.
f(x) is the actual amount of servo deflection and depends on the actual stick deflection x
(0=center and ±1 full stick deflection)
the amount of exponential p (0=0%, -1=-100% and +1=+100%).
e is the well known constant (2.718).
If we want f(0)=0, we will have th change this into f(x)=ep x-1.
Furthermore, p=1 doesn't give a very steep knick, so
we can be pretty sure that 100% exponential will not result in p=1 but some higher
value. So we introduce a linear scaling factor B, giving f(p,x)=eB p x-1.
In the next section we will measure B from the actual transmitter behaviour.
Finally, we want that f(1)=1, and therefore we divide f(p,x) by f(p,1), giving our
final formula
e-B p x-1
f(p,x)= ----------------
e-B p-1
Probably this formula is also approximately right for other transmitters,
although B will probably different for various transmitters.
Please mail me the value for your transmitter if you estimated the value,
so that we can collect the right values here.
To do this we need something that can convert the servo output into a number.
I don't have equipment for that, and on top of that my servos are currently
at Futaba for checking, so I decided to read off the servo position with the transmitter setup
my TruFlite flight simulator, which shows the 'servo' deflections
in real time with a bar graph. This is a very rough interface,
where you can read the servo deflection with an accuracy of roughly 10%.
First we set the ATV of the transmitter to 100%. Then we checked the servo
deflection when we deflect the stick with 70% and -70%. This is also a rough estimate,
we can accurately set the stick to the second tick which I guess to be the
70% point, because the stick just can't reach the third tick where the 100% would be.
I found the following results for various settings for the elevator exponential:
0% expo gives -60 and +80
50% expo gives -70 and +90
100% expo gives -90 and something >+100
-50% expo gives -50 and +65
-100% expo gives -35 and +50
It seems that the midpoint is off, probably because the TruFlite interface is so rough (hope
it's not my transmitter sticks!).
So we substract 8 from all values to correct this:
0% expo gives -68 and +72
50% expo gives -78 and +82
100% expo gives -98 and +100?
-50% expo gives -58 and +57
-100% expo gives -43 and +42
Now we make a table with B set to 2, 2.5 and 3:
| f(p,70) | p=-100% | p=-50% | p=0% | p=50% | p=100% | B=2 | 0.480369 | 0.592239 | 0.702097 | 0.798115 | 0.872584 | B=2.5 | 0.427761 | 0.564545 | 0.702621 | 0.81931 | 0.901406 | B=3 | 0.378353 | 0.536918 | 0.703144 | 0.83901 | 0.924769 |
Comparing these values with the measurements shows that B=2.5 seems the best approximation. Of course more accurate measurements would allow more accurate estimation of B.
We estimate the function of the exponential of the FF8s to be
e-2.5 p x-1
f(p,x)= ----------------
e-2.5 p-1