reversed exponential

Many of us use exponential and know what it does.

I use it to soften the middle of the stick while maintaining full deflection for aerobatics. This seems to be what everyone else does according to what I've read online.

However, the radios I've seen are capable of going the other way - making the center of the stick touchy as a hornets nest with full deflection mushy.

My question is, is there a use for that? If not, why have it?


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Because if you're writing software for a computer radio, it's super easy to put in. And if you write software for anything that has to do with a human controlling a computer, you learn that even if a feature is the stupidest thing in the entire &*@% _universe_, there are users out there who won't believe you until _they_ dial it into _their_ system and go do some damage with it.

Then they get back to you and say "This is the stupidest thing in the entire &*@% _universe_! Why did you put it in!". But they only do it once, which is a lot less complaints than you get if you don't put it in.

Who, me? Cynical?

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Tim Wescott

Tim Wescott wrote in news:aL- dnf794I5IMpfQnZ2dnUVZ

Which I am.

I have a working expo calculation, but it does freaky things if I do reverse expo. But it dawned on me, why bother with reverse expo at all?

I can still make it happen with a little extra code.

Although the microcontroller I'm using is quite fast and powerful, there's no point wasting clock cycles on something that's not necessary.

But then, maybe I should put it in there anyway, for the just-in-case department.

Nahhhhh.... I woulda nevuh guessed. :)

I did do a quick search after posting specifically for reversed expo and found a discussion where some were using it on their throttle channel to linearize the response of their turbine engines. But several also said they just do it with a throttle curve.

Thanks for that. Interesting fellow.


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Exponential allows a rotary servo to mimic a linear servo. Therefore, reverse exponential will allow you to use a linear servo and mimic a rotary servo.

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One of the top glider pilots in my club uses reverse expo to make the middle very sensitive. This is his normal method of flying. However I have found it very difficult to fly his planes because they are so sensitive. But he loves it.


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Ed Anderson

I can think of one use and one MAYBE use.

Reverse expo on the aileron channel when using flapperon mixing where the aileron mix has lots of response when the flap is down.

And MAYBE on variable pitch blades, to make things a bit more bitey around the middle of the stick. Did something very similar in a custom mixer board for an indoor dirigible. The throttle stick centered had 0 blade pitch and no throttle as the stick was moved from center the motor throttled up and the blade pitch was set forward or backwards to change directions. The only way to get smooth response was to do a bit of reverse expo on the blade pitch.

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You can do a pretty good approximation of exponential by making an input/ output relationship that goes

y = (1-a) * x + a * x^3

Assuming that x works in the range [-1, 1] (normalization is up to you), this means that for a in (0, 1) this gives a nice controllable softening of the response around zero, with a steeper curve as you get the ends. It also means that for a = 0, y = x (i.e. zero means no exponential). To make it work with "negative" exponential you just need to allow a to range down to -1/2 (any further and y will peak before you run out of range of x). As long as you have signed arithmetic, this should work just dandy.

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Tim Wescott

On Sun, 19 Dec 2010 11:47:37 -0600, Tim Wescott wrote in :

That looks ambiguous to my untrained eye. Do you need more parens?

y = (1-a) * x + a * x^3 y = ((1-a) * x + a) * x^3 y = (1-a) * (x + a * x^3) y = (1-a) * x + (a * x^3) y = ((1-a) * x) + (a * x^3)


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Martin X. Moleski, SJ


Standard mathematical hierarchy -- exponentiation first, then multiplication (and division), then addition (and subtraction). so apply all those, and you get

y = ((1-a) * x) + (a * (x^3)),

only with fewer parentheses cluttering things up.

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Tim Wescott

The only reason I can think of is if you happen to have something that is a bit mushy around the center, perhaps reverse expo would make it more responsive.

I have a JR8103 radio that has acceleration mixing, doesn't seem very useful. I used it on a helicopter tail rotor for a kind of torque feed-forward for the LMH-110 mechanical gyro, it seemed to help quite a bit. As I increase throttle, it applies a little extra tail rotor depending on how fast I increase the throttle. Probably no use today with the heading hold gyros, but it helped the heli I used it on.


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I use it on the throttle channel for my glow engine models to make it more responsive around the lower end of the stick travel. I like it a lot.

Good flying, desmobob

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Robert Scott

Tim Wescott wrote in news:YIidnWDJU9Sk2JPQnZ2dnUVZ

Thanks for the hint. But, I did manage to get a real exponential curve. It just took my brain a little longer than usual to figure it out. Must be getting rusty. I've done it before and finally pulled out some old code of mine to refresh from.

The basic formula is very direct...

out = in^expo

Where the exponent value ranges from .1 to 10 so that,

-100 equals an exponent of .1 0 equals 1

+100 equals 10.

Obviously logarithmic, so I had to do some other massaging of the numbers to make things come out as expected. And yes, normalization makes it much easier.

Anyway, I'm glad I asked cuz I'm now informed on some reasonable uses of reverse expo. Thank you everyone.


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