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Dec 10, 2014, 12:00 PM
Lion Whisker
Thread OP
Yah dudes! Clutter away. I'm proud to have started such an envolved thread. I'll just ask a question again if I can't find the answer. Thanks T for the tip on the computer fan. I'm also thinking of doing some serious air flow tubing from the front grill! >
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Dec 10, 2014, 04:32 PM
Stunt man
Dr T's Avatar
Alright, if you guys insist .

Got my crayons out and did some philosophizing... I think Solo and I were both partly right, but were generalizing a bit too much outside of our own experience zone .




Pic shows the two situations we mixed up, difference being the level of traction relative to the wheel axle Torque the motor is able to produce. As a little background, note that a permanent magnet DC motor (so both brushed and brushless) is characterized by a linear relationship between stall Torque when the Torque is maximum with the shaft at standstill and no-load speed with no applied shaft Torque and maximum output speed. This is fundamentally different than with combustion engines, and the reason why so many people make mistakes about PMDC motor Torque and gearing.

The green and blue lines represent the wheel axle Torque based on 2 different gearings (green gearing, g1, is 25% higher than blue gearing g2: you can see the no-load speed of g2 being 25% lower than g1, and the stall Torque of g1 is 25% lower than g2; surface areas under the triangles are equal, as they're both produced by the same motor). The orange lines represent the wheel axle Torque required for maintaining a certain speed, which follows from the the sum of the rolling resistance (increases linearly with speed) and the aerodynamic drag (increases quadratically with speed). I chose the wheel axle Torque as reference frame instead of the motor shaft Torque, so the orange lines would stay constant and the reference to the real world would be more clear (taking motor shaft as reference would have resulted in one motor Torque line and two Required Torque curves, one for each of the different gearings - doesn't matter much, but I think this is easier to interpret).

The amount of Torque represented by the difference between the green, resp. blue lines and the orange line is the excess Torque that will cause the drivetrain and wheels to spin up more. The points where the green resp. blue lines cross with the orange line is the equilibrium between what the motor can produce and what Mother Nature wants on return for travelling at a certain speed; the corresponding speed is the steady state (zero acceleration) end speed, or real world top speed. The max traction Torque is the physical limit on the amount of wheel axle Torque that can be converted into actual longitudinal car acceleration, this is represented by the red dotted lines. As long as the green and blue lines exceed the max traction Torque, the throttle needs to be feathered (reducing motor input Voltage) in order not to lose traction. The part of the excess Torque that exceeds the "usable" part, will be used for the angular acceleration of driveline and wheels, but the car will simply not be able to keep up with that and will not accelerate faster longitudinally (car acceleration will actually reduce as traction reduces with too much slip).

Now, situation 1 represents motors with a very large Torque overhead compared to the max traction Torque. In this situation, the higher geared set-up will actually be able to pull along max traction even longer than the lower geared set-up. Until the blue line drops below max traction, the longitudinal car acceleration of both set-ups will be completely equal, but after that, the lower geared set-up will start reducing acceleration (and max throttle can be applied without losing traction), while the higher geared set-up can continue acceleration still a bit at max traction rate (with still the need for throttle feathering).

Situation 2, with more moderate wheel axle Torque levels compared to traction, seems to be corresponding to Solo's example. Both set-ups are able to break traction from a dead-stop, but in this case it's the high geared set-up that starts to drop below the max traction first, from which point the lower geared set-up will accelerate the car faster than the high geared set-up.

Cross-over from situation 1 to 2 happens where the wheel axle Torque lines of the different gearings cross.

Edit:
I just realize something funny with situation 2: while the acceleration of the car is higher for the low geared set-up between the speeds where the green / red and the green /blue cross, the acceleration of the high geared set-up will be higher after the blue/green cross-over again... high gearing FTW!

That was fun !

Some background references I found useful in understanding this:
  1. http://www.johnsonelectric.com/en/re...mdc-motor.html
  2. https://evmc2.wordpress.com/2014/07/...nd-hp-ratings/
  3. http://www.asawicki.info/Mirror/Car%...r%20Games.html
  4. http://www.completepowerelectronics....dc-pmdc-motor/

Cheers!
Last edited by Dr T; Dec 10, 2014 at 05:00 PM.
Dec 10, 2014, 10:06 PM
Lion Whisker
Thread OP
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Dec 10, 2014, 11:46 PM
Cookie
10x8's Avatar
the string
Last edited by 10x8; Jan 12, 2015 at 12:46 AM. Reason: info
Dec 11, 2014, 01:15 AM
Fan of just about anything RC
SoloProFan's Avatar
Quote:
Originally Posted by lukebluske
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Well, you asked for it.

But don't worry, though I think a picture often says more than a 1000 words, I do need to read that graph and accompanying text a few times to get the idea I think I may understand what it says. I tend to look at it more from the physics angle. When the wheels are slipping, the car will only accelerate well if this slipping stops, before that you are just spraying dirt to the back, or burning rubber, both spectacular, but not very effective when you are trying to get up to speed as fast as possible. Compare like driving on ice, or with a really loose slipper clutch.

When you have 100% traction, and no slipping wheels, I fall back to the simple equation that a force (called "F") to achieve a certain acceleration (called "a") is related to the mass of the vehicle (called "m") as follows. "F" equals "m" times "a"

So if you increase mass of a vehicle, you can re-work the formula, and see that "a" equals "F" devided by "m". If "m" increases, the calcalated "a" will decrease, so the car will accelerate slower.

In an RC car, if you use a bigger pinion, you reduce torque, and this results in a smaller force F to accelerate the car. So acceleration will suffer. By how much depends on the motor's performance and mostly it's torque.

But this only applies in a zero slip situation, so all rotation of the motor is used effectively and nothing is wasted in the wheels "struggling" for traction. If a driver just guns the throttle, and have wheelspin, or the surface is very slippery, like a wet track, or ice, you will usually get moving faster with less torque, just like in a real car, where on a slippery road, the advice is often to shift up to 2nd gear, so you won't have to "feather" the gas pedal beyond most driver's capability.
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Dec 11, 2014, 04:10 AM
Stunt man
Dr T's Avatar
All I said is based on Physics Solo, I omitted the formulas on purpose not to make it all look too scary . Torque is just the rotational cousin of Force (with moment of Inertia "I", and angular acceleration "alpha" as the rotational counterparts of the longitudinal "m" and "a") and they're directly (proportionally) related through the "arm's length" or radius (e.g., wheel radius) at which they are applied. Check the "Physics for car simulation" link I provided, it gives an understandable overview of all the equations and factors involved, the part about traction as function of wheel slip is very interesting (there's always some slip, without there can be no traction Force) - be careful though: it is written for combustion engines, so don't let the Torque curves confuse you, they're fundamentally different than the PMDC curves, which is probably the sole reason we're having this discussion. If you write out and use the equations, you'll end up with what I posted (because I did ). If not, we can compare results and continue this awesome quest .
Last edited by Dr T; Dec 11, 2014 at 05:00 AM.
Dec 11, 2014, 05:48 AM
Fan of just about anything RC
SoloProFan's Avatar
More scary with formulas? I thought it was scary enough already.

Torque is indeed related to force, as the wheels translate the motor's torque to forward motion. I don't see how slip is needed for traction though as you state here:

Quote:
Originally Posted by Dr T
the part about traction as function of wheel slip is very interesting (there's always some slip, without there can be no traction Force)
If we were to replace the wheel with a gear, and the road by a long gear rack, like you see on those mountain climbing trains for instance, you will elimitate slip totally, but have 100% traction by default. That would imply, taking that slip is needed for traction, that the train will never start moving.

In that situation, it should be only a matter of how much force results by rotating the gear by the motor's torque, and then it would be a simple matter of the formula F = m *a, or a = F/m, to calculate the acceleration. Though we should also include drag and friction, which exert a counter force, that is not constant but speed dependent, and also on the shape of the vehicle, as airflow may alter when it moves beyond a certain speed. So calculating isn't as easy as it seems, even in a theoretical zero slip situation.

With cars there is always some slip, even if the tire "sticks" to the road, the tire itself will deform under hard acceleration, not just ballooning, but also be able to rotate slighly in respect to the rim. So calculating an acceleration curve, based upon the motor's throttle curve, will be hard, if not impossible to get fully accurate. Measuring tests would probably yield better, more practical results, but will be hard to make consistant, as the driver may one run apply throttle faster than the other, and have less or more wheelspin.

I think the best way to determine how much gearing affects acceleration, is to eliminate as much variables as possible, so going back to that gear and gear-rack, and performing the test in vacuum to eliminate drag. Also, you would need some levitation system, since if a vehicle rests on it's "gear-wheels" it won't have perfect gear mesh, and this induses extra friction, just like when putting pinion and spur too close together. You will then only have bearing friction on the gear axles and motor, and friction between the gear and gear-rack as factors "polluting" the results, but I bet the overall picture will be that lower gearing will give better acceleration to a certain set top speed, as long as the gearing isn't such that this top speed can't be reached, because even at top motor rpm, the vehicle will run slower.


And now my brain needs to cool down, or it stars "slipping" lol
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Dec 11, 2014, 07:47 AM
Stunt man
Dr T's Avatar
Quote:
Originally Posted by SoloProFan
If we were to replace the wheel with a gear, and the road by a long gear rack, like you see on those mountain climbing trains for instance, you will elimitate slip totally, but have 100% traction by default.
What you're saying here is not wrong, but it does not apply to tire/surface contact, simply because... a tire on the road is not a gear on a gear track. Here's a useful quote out of one of the background links I added (it's referring to 2WD, don't let that confuse you):

Quote:
In a typical situation where the car is cruising at constant speed, the rear wheels will be rotating slighty faster than the front wheels . The front wheels are rolling and therefore have zero slip. You can calculate their angular velocity by just dividing the car speed by 2 pi times the wheel radius. The rear wheels however are rotating faster and that means the surface of the tyre is slipping with regard to the road surface. This slip causes a friction force in the direction opposing the slip. The friction force will therefore be pointing to the front of the car. In fact, this friction force, this reaction to the wheel slipping, is what pushes the car forwards. This friction force is known as traction or as the longtitudinal force. The traction depends on the amount of slip.

[snip scary formula]

The relationship between longtitudinal (forward) force and slip ratio can be described by a curve such as the following:

Your "gear on gear-track" analogy would represent infinite max Traction, so no red-dotted line in my earlier plots. This would be the equivalent of an electric RC car situation in which the max traction Torque would exceed the wheel axle stall Torque (i.e., the car is not able to break traction -slip ratio stays below the "bend" in the quoted graph-, even at WOT from stand-still). In that case, you would indeed see the low-geared set-up accelerate faster, until the speed where the blue and green lines cross, from which point the high-geared set-up accelerates faster.

The typical modern brushless system can produce so much more Torque than the max traction Torque though, that such a scenario is very unlikely and might only apply remotely close to something like RC tractor pulling (if such a thing exists).

EDIT:
Quote:
Originally Posted by SoloProFan
Though we should also include drag and friction, which exert a counter force, that is not constant but speed dependent, and also on the shape of the vehicle, as airflow may alter when it moves beyond a certain speed.
Yes, that's the orange line in my graphs, it's the sum of the rolling resistance (proportional to speed) and aero drag (quadratically dependent on speed).

Driveline friction (bearings, binding, etc.) is proportional to drivetrain rotational speed and is not in my graphs, because I took wheel axle Torque as frame of reference to make it easier to comprehend. Would I have taken that into account, then that would actually slightly penalize the low-geared set-up, as it needs higher motor RPM (and thus higher motor bearing friction higher losses) for the same speed, compared to the higher geared set-up, so it would not change my conclusions. Aerodynamic properties, as well as air density equal out because we are comparing identical set-ups in identical environements. Drag is proportional to aerodynamic surface and coefficients, so the orange line would just steepen (worse aero) or become less steep (better aero) when changing aero properties. All the principles would still hold.
Last edited by Dr T; Dec 11, 2014 at 08:38 AM.
Dec 11, 2014, 08:30 AM
Fan of just about anything RC
SoloProFan's Avatar
Sounds ok, but indeed that would only apply to 2WD, and maybe 4WD with center diff. With full time 4WD with no center diff, there is no way the rear wheels can move faster, unless things start skipping teeth in the drive train. All assuming rear and front tires have same diameter, which is mandatory for driving a full time 4WD with no center diff on a high traction surface where there will be very little slip. As otherwise there would be strain building up between the front and rear, or one pair of tires will be in constant slip, even at steady speed, which is not very desirable, I think. On loose dirt, it's a different thing ofcourse, then there is constant slip of all 4 wheels, and other physics apply, leaning more like running on ice or indeed tractor pulling, where lots of slip are needed.
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Dec 11, 2014, 10:45 AM
Stunt man
Dr T's Avatar
You're over-thinking it too much, the quote about the rear tires is just explaining how slip on any "driven" (receiving axle Torque through some kind of motor or engine) tire is the cause of longitudinal Force, nothing more, nothing less. It applies to all types of surfaces.
Dec 11, 2014, 01:59 PM
Fan of just about anything RC
SoloProFan's Avatar
Quote:
Originally Posted by Dr T
You're over-thinking it too much, the quote about the rear tires is just explaining how slip on any "driven" (receiving axle Torque through some kind of motor or engine) tire is the cause of longitudinal Force, nothing more, nothing less. It applies to all types of surfaces.

Over-thinking? Lol, you got me started with those graphs and deeper mechanics.


Let's keep it more practical then. If you manage to keep the wheels from spinning as much as possible, so almost all of the rollout of the tire results in forward motion, the gear ratio will affect acceleration. But gear it too low, and you get more like a crawler, insane torque, but no top speed. Gear it up to the moon, and you get a car that goes very fast, but takes forever to reach that speed, provided the motor doesn't burn out before that happens. Between those extremes is a "gear ratio band" where the motor is happy, and you fine tune the car's throttle response for a little better punch coming from the turns for instance, or a little better straight line speed.
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Dec 11, 2014, 04:42 PM
Stunt man
Dr T's Avatar
Quote:
Originally Posted by SoloProFan
Let's keep it more practical then. If you manage to keep the wheels from spinning as much as possible, so almost all of the rollout of the tire results in forward motion, the gear ratio will affect acceleration.
No, the mistake you make here is you assume the maximum traction changes too with the gear change, it's not, meaning none of the wheel axle Torque you gain from gearing down, can be put to use, as the high-geared system had already more Torque than necessary for breaking traction, that's what the plots are all about.

Edit:
I think the crux here is to understand that max traction (determined by tires, surface and weight of the car) can not be increased by feathering the throttle. The max traction Torque or Force determines the macimum accelaration that is physically possible given a set of tire/surface conditions. By using throttle feathering you try to stay as close to the max traction limit as possible as that yields max acceleration for those tire/surface conditions, but you can't increase max traction by throttle feathering and it is not dependent on gearing.
Last edited by Dr T; Dec 11, 2014 at 06:05 PM.
Dec 11, 2014, 06:18 PM
Fan of just about anything RC
SoloProFan's Avatar
Quote:
Originally Posted by Dr T
No, the mistake you make here is you assume the maximum traction changes too with the gear change, it's not, meaning none of the wheel axle Torque you gain from gearing down, can be put to use, as the high-geared system had already more Torque than necessary for breaking traction, that's what the plots are all about.

Somehow there is a thing is this reasoning that doesn't add up. As tests with different gearing always yield changes in accelleration, at least on surfaces with good traction. I think it has something to do with the breaking traction situation that makes things seem to contradict. If the motor has so much torque it will break traction at every rpm, so during the entire acceleration phase, then gearing down won't help indeed, as the wheels are already constantly slipping a lot. This can be compared to driving on loose dirt for instance. I think this is the situation you are referring to, and indeed, extra torque will not result in better acceleration. It's like trying to get a car up to speed on ice, as soon as the wheels start to slip, lower gearing won't help the car get to speed faster.

But if we take a high traction surface, things are different, I think. When coming from standstill, and giving full throttle, there may be some wheelspin, and extra torque can't be put into extra acceleration at that very moment. But after a few seconds at most, if good tires are used, and we're talking a high traction surface, but let's say, asphalt, the wheels will stop slipping so much, and have an almost 100% traction situation, or at least, better traction than in the phase where full throttle was applied from standstill. In this case the motor has enough torque to break traction, but not during the entire acceleration phase, only in the very beginning.

I think you can compare this to braking, as it's basically the reverse of accelerating. When you get the wheels to lock, the car slides forward, and extra braking power, like having bigger and better brakes, won't help, the only thing slowing the car down is the friction between road and tire. So the maximum traction, or in this case, lack of it, and since the wheels are already locked, the braking power (torque) won't improve deceleration, since the wheels just slide over the surface. But when ABS is applied, so the brakes are operated in a way that the wheels don't lock and don't start to slide, but keep traction, the car will slow down much better, and the tires will have better traction, though the road conditions are the same. And in that case you can see a difference between weak brakes and better ones, even though the weak brakes still have enough braking power to make the wheels lock and the car start to slide in a low traction surface condition. And just like with acceleration, if you "feather" the brakes, you also get better deceleration, than if you just stamp the brake pedal down, instantly locking the wheels, and rendering the brakes useless. If you throttle up to fast that the wheels keep slipping, you are equally not using all the motor's torque, whereas you can get the car accelerating better if you increase rpm a little more gently.

Indeed you can't increase max traction, but as soon as you throttle up so fast that the wheels start to slip, and keep slipping, you are not getting as close to max traction as you would with a more gently increase of throttle.
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Dec 12, 2014, 09:28 AM
Stunt man
Dr T's Avatar
Quote:
Originally Posted by SoloProFan
Somehow there is a thing is this reasoning that doesn't add up. As tests with different gearing always yield changes in accelleration, at least on surfaces with good traction. I think it has something to do with the breaking traction situation that makes things seem to contradict. If the motor has so much torque it will break traction at every rpm, so during the entire acceleration phase, then gearing down won't help indeed, as the wheels are already constantly slipping a lot. This can be compared to driving on loose dirt for instance. I think this is the situation you are referring to, and indeed, extra torque will not result in better acceleration. It's like trying to get a car up to speed on ice, as soon as the wheels start to slip, lower gearing won't help the car get to speed faster.
Approach this stuff from the Physics perspective and it will add up. As my plots show, you don’t need a set-up that can break traction at every RPM (that is actually Physically impossible) to end up scenario 1: the ability to break traction at half or even less (depending on how much gearing is changed ) of the peak RPM is enough.

I refined the plots a bit based on your comments, so they should be less prone to misinterpretation.



You can see that the theory perfectly explains both of our views. The tests you speak of, are represented by the green zone in plot 2. However, it clearly shows that the "lower gearing equals higher acceleration" adagium that is so commonly used, actually is an over-generalization as it applies to a limited part of the speed range (I added plot 4 to show how this speed range -which is defined on the right side by the cross-over point-, at which lower gearing might increase acceleration, reduces with lowering gearing more) and under circumstances in which the powerplant has little Torque overhead compared to available traction (i.e., cross-over is below max traction).

I added plot nr. 3 to clarify that my scenario 1 is not just about driving ice or loose dirt, it applies to any set-up that has a considerable (cross-over above max traction) Torque overhead compared to the level of traction that is accommodated by tires/surface. This may indeed not apply to typical competition level set-ups (where powerplant needs to be light and any overhead relative to what is needed, would only be a waste of handling, as heavier and too easy to break traction ). However, for the typical modern recreational brushless set-up, it is less far-fetched than what, based on you feedback, I assume you might think.

Here's a little video of a truggy I have:

126 km/h (78 mph) 6S Brushless 8ight Truggy on-board view - with GPS speedo (2 min 42 sec)
.

I need carefully build up throttle/speed, well past half of top speed in order not to break traction and make things going sideways. I know that surface sucks compared to on-road tracks and tires balloon way too much (reducing contact area and thus traction), but it's far from being ice or loose dirt and I'm not running Crawler gearing either . Also, I recently geared down my mini 8ight, running a 6-pole outrunner on 4S (it's not brute, it's efficient ), from 67 mph to 50 mph, as a 60+ mini appeared not to be that practical for playing with my small kids , and I saw no increase in acceleration, simply because the 67 mph set-up would still break traction beyond the speed range where the lower-geared set-up would have topped the high-geared set-up on wheel axle Torque. I realize these are just two of my limited experience examples, and I am not running very typical set-ups (I have a Losi 22T running a 3660 motor on 6S too, and will be using a 5682 motor in my GT2... blasphemy!!! ), but it does happen to correlate nicely with Castle’s marketing mumbo jumbo regarding their popular, wide-spread and thus not so exotic brushless systems:

Quote:
High power capability brushless systems can act very differently than brushed systems and even differently than other brushless car systems. Where you used to approach gearing from a sense of managing the torque of the motor (smaller pinion gives the motor more torque), in this system you’ll need to look at gearing only as a simple matter of top speed at full throttle. For example: If you are not able to get up to full throttle on the longest straight at the track (car is too fast) you should gear down to the point at which you are actually using the whole range of the throttle trigger including full throttle at times. If you never get to full throttle, or have to dial down your throttle EPA, you are running the system hotter and with less runtime than you could have if you geared down. So again, think of gearing only in terms of what speed you can actually use at full throttle.
A high power capable brushless motor in electrical engineering and physics terms, has unlimited torque. We live in “the real world” so technically for us that’s not totally true, but – a brushed motor has a torque level that due to its design has an upper limit, regardless of how much power is being applied to it. That limit is low enough that you can see it clearly on an average track On the other hand, a high power brushless motor’s limit to torque in an RC vehicle is not within the bounds of the motor itself so much, but rather falls on the ability of the battery to deliver current to it.
The “Where you used to approach gearing from a sense of managing the torque of the motor (smaller pinion gives the motor more torque), in this system you’ll need to look at gearing only as a simple matter of top speed at full throttle” is exactly what I mentioned to Luke in my first post in this thread: there is not really a trade-off between top-end and acceleration, assuming a typical modern LIPO powered brushless set-up (I’ve learned I need to add that last part now, when making that statement in future ).
Last edited by Dr T; Dec 14, 2014 at 01:11 PM. Reason: Revised pic, red zones do not exceed equilibrium speed anymore now.
Dec 12, 2014, 10:40 AM
Fan of just about anything RC
SoloProFan's Avatar
I see your point, but I think it all comes down to that we differ on what to consider a "typical brushless setup". For me that is a setup that can only break traction at low rpms, coming from standstill, or only just after that. And in that range, gearing does affect acceleration, though not as pronounced as with a typical brushed setup.

Setups like that 6 pole outrunner on 4s in a Mini 8ight (insanity, total insanity, lol) have so much power, you can break traction at much higher rpms too, and then gearing down won't affect acceleration, but only affect top speed. My testing never involved a setup with as much massive torque overhead as your examples, hence the different observations. So the theory holds but we both had different setups in mind.

Maybe the line should be "assuming a typical high torque, somewhat overpowered, brushless setup. I get the feeling that 6 pole outrunner on 4s may have more power than a typical inrunner setup on a 1/8 scale buggy.

Heck, I run a 4 pole inrunner on my LC Racing Emb buggy, which is the same size as the Mini 8ight, and on 2s that is already a blast.
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