What exactly does expo percent mean?

[Allan Bennett]

I'm sure we all know in general terms that dialling in some expo to a control will dampen its response around the mid-stick area. But what exactly do the numbers mean?

Assuming that the regular stick response is represented on the X-Y axis by a straight line going from -100 to +100, crossing the axis at 45 degrees, does 20% (or should it be -20%?) expo mean that it will cross the X axis at 80% of 45 degrees, i.e. 36 degrees? And how do we know how far either side of centre the reduced slope extends before it actually becomes an increased slope in order to reach the full-stick 100% position?

Is there a standardised formula for the curve, or does each radio manufacturer (and OTX) do their own thing in this respect?

[Ron Gray]

Hopefully these 2 screen shots will 'explain' it better than words. (Taken from OpenTx)

[Allan Bennett]

That's interesting Ron that you've used OTX to illustrate it, for it had crossed my mind to use curves instead of expo + rates. But the way you've shown it is not the way I understand it to be, for those curves show a slow start, increasing all the time, rather than decreasing around the centre point like this:

But my question is, assuming I'm right on the shape of the curve, is there a standard formula used by manufacturers, which determines how 'flat' it gets at the centre point and how far either side of the centre point the 'flat' portion goes?

[Dickw]

Posted by Allan Bennett on 01/09/2020 08:35:39:

That's interesting Ron that you've used OTX to illustrate it, for it had crossed my mind to use curves instead of expo + rates. But the way you've shown it is not the way I understand it to be, for those curves show a slow start, increasing all the time, rather than decreasing around the centre point like this:

...................

But my question is, assuming I'm right on the shape of the curve, is there a standard formula used by manufacturers, which determines how 'flat' it gets at the centre point and how far either side of the centre point the 'flat' portion goes?

Yes you can use curves to recreate the equivalent of expo on a control, but it always seems easier to simply use the expo function.

I don't believe there is a standard way of expressing expo as a percentage, and I have never seen any explanation of what it is a percentage of. My experience is that the expo value is brand specific.

Dick

[Bob Cotsford]

Nasty memories of O level maths are surfacing, exponential and logarithmic functions. I suspect there is a base calculation relating control deviation to stick deflection on a logarithmic basis which is taken as 100% expo, and the 'expo' value we see is the % of this true exponential curve that is mixed with a linear response to derive our output curve, though this will be approximated to varying degrees and even the basis used for the 100% calculation will vary between manufacturers and even tx models. I seem to remember that on Futaba's FF7, 8 and 9 expo was actually a two stage ramp and the expo value defined the amount of deflection at which the ramps changed from shallow to steep. Then there's the question of how a manufacturer defines +ve and -ve expo - can of worms anyone?

[Gary Manuel]

If it's an actual formula you are looking for, the following info from a google search might be of interest:

With 20% of exponential, the resulting curve will have 80% of the slope at the center of control, i.e., it would now feel like 80% of throw when the stick is near the center. As the stick moves to the edge, the slop deepens, and you still get the full throw.

In a dual- rate setting, if your low rate is at 60% throw linear, and your high rate is at 80% throw with 25% expo, since 80% x (1 - 25%) = 60%, the stick will feel the same around the center in both high rate and low rate.

By the way, the curve is not really exponential. With OpenTX, since it is open source, we know the formula to be
y = e * x^3 + (1-e) * x
(e being the exponential rate)

While Spektrum's formula is not public, I suspect it to be
y = e * x^4 + (1-e) * x, for x >= 0
Flip the sign for x < 0.

Note in both cases, the slope at x=0 is (1-e).

Edited By Gary Manuel on 01/09/2020 12:45:06

[Gary Manuel]

The way I understand it from the formulae above, if you extend the line of the curve from around the centre point as shown in RED below, the value of expo is the amount that the throw is reduced from the maximum value of Y. In this case the expo is about 80%. I've learnt something today and it all makes sense now.

[Allan Bennett]

Nice that your transmitter shows a curve Dick -- I assume your screenshot is from your Tx. It would be nice if OTX could to that. It looks like there you can set up different values for the + and - parts of the curve and it looks, to my eye anyway, that with 50% dialled in the curve is at approximately half the slope of the straight line at the mid point.

On another forum recently I was in a discussion about settings on a flight controller for a flybarless heli, in which I learned that its firmware incorporates expo in the major controls by default, to mimic a linear servo response, bearing in mind that a normal rotary servo gives more sensitivity in the 90-degree position than at the ends of its travel.

I seem to recall that my Futaba used negative expo numbers to soften the curve at the centre so, as you say, it's probably different for each manufacturer.

Edit:  I went for lunch while typing, during which time the last two very informative posts came in.  Thank you.

 

Edited By Allan Bennett on 01/09/2020 13:24:49

[Bob Cotsford]

I'm pretty sure (allowing for vagaries of memory) that OpenTX/Companion used to show a curve when expo was selected. I see 2.3.9 Companion doesn't do this, I'll have to fire up a tx to see if it does it in the tx editor.

[Dickw]

Posted by Allan Bennett on 01/09/2020 13:22:27:

Nice that your transmitter shows a curve Dick -- I assume your screenshot is from your Tx. It would be nice if OTX could to that. It looks like there you can set up different values for the + and - parts of the curve and it looks, to my eye anyway, that with 50% dialled in the curve is at approximately half the slope of the straight line at the mid point.

........................................

Yes, screen shots are from the Tx, and you can set up different rates and Expo for the + and - parts of the curve.

Looking at Gary's diagram I think he has it about right and the Expo is the reduction in throw shown by extending the line of the curve from around the centre point. 100% Expo would give me a "deadband" either side of stick centre - see screen shot. No idea what the formula for the curve on mine is though!

Dick

[Ron Gray]

Rather than just showing curves, as I did above, here is the expo curve in OpenTx (Companion)

[Bob Cotsford]

Is that from the simulator Ron? I must try it sometime .

[Ben B]

It's a good question! I've never assumed there was an agreed standard on expo percents. Then again now mostly flying quads so have to deal with expo, rc rates, super rates, feed forward, pid loops... I don't even know what half of them do let alone whether they are standardised!!!!

[Martin McIntosh]

You don`t need fancy curves or anything like them. Just try it. On any new model I always dial in 30% on low rate and 40% on high (+ve for JR/Spektrum and -ve for Futaba). All you will notice is that the model is much less sensitive to small stick movements around centre and you will still have full travel available if you need it. Best thing ever invented for model control.

[Ron Gray]

@Bob - from Companion simulator, looks very close to real thing!

@Martin - the curve is generated as a result of entering 30% for expo.

[The Wright Stuff]

Does this help?

This is a few years old, but may still be relevant...

[Mike Etheridge 1]

 

DELETED POST

Edited By Mike Etheridge 1 on 01/09/2020 21:18:22

Edited By Mike Etheridge 1 on 01/09/2020 21:19:23

[Gary Manuel]

Posted by The Wright Stuff on 01/09/2020 21:08:39:

Does this help?

This is a few years old, but may still be relevant...

It helps to complete the picture. My earlier post gave the formula for OpenTX (fact) and Futaba (assumed). This link gives a formula for JR (assumed) as:

Y = (Exp/10)E-05X^3 + (1 - Exp/100)X

where,

Exp = expo expressed as a percentage

E = exponential constant - 2.718

This can be converted to the same format as OpenTX and Futaba as follows:

our expo "e" is a "per unit" value, rather than per cent = Exp/100, therefore,

Y = (e*10) * (2.718-0.5) * x^3 + (1-e) * x

Y = 22.18e * x^3 + (1-e) * x

The second part of the formula [(1-e) * x] is identical to the other two formulae. It is predominately this first part of the formula which describes the curve around the centre point, so the earlier discussion about the relationship between the expo value and the slope around the centre point still apply. The first part of the equation [22.18e*x^3] describes the curve as it progresses from the initial slope towards the maximum value. JR and OpenTX are cubic (x^3) polynomial whereas Futaba is quartic (x^4) polynomial. This difference will have minimal effect on the feel of the sticks.

To all intents and purposes, we can assume that the expo value of all three brands have the same meaning (ignoring the +ve / -ve value difference).

Edit - actually, looking at the JR formula from the link it doesn't look right! The value of the first part should never exceed unity, but it does. Not convinced that BEB's formula is correct.

Edited By Gary Manuel on 01/09/2020 22:58:27

[Gary Manuel]

Just for completeness, here's what the OpenTX (red) and Futaba (green) formulae look like when plotted in an excel spreadsheet. Note that x^3 and x^4 are just labels for the two curves and not the full formulae, which are y=e*x^3+(1-e)*x and y=e*x^4+(1-e)*x respectively. In summary, the Futaba gives a slightly wider soft area in the central portion of the stick, with a more severe climb towards maximum limit than the OpenTX system (and JR despite the incorrect formula would be my guess).

20% expo

40% expo

60% expo

80% expo

100% expo

Edited By Gary Manuel on 01/09/2020 23:58:38

[Gary Manuel]

Enjoyed getting the old brain cells working again.

I'm done now.

[Allan Bennett]

Thanks for all that analysis Gary.  What a shame we didn't have electronic spreadsheets when we were doing O-levels 

Edited By Allan Bennett on 02/09/2020 08:15:25