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Theoretical Speed & Distance Curves

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One of the aspects of selecting a proper gear-ratio is understanding the trade-offs between acceleration, top speed and power consumptions. To that effect, I've been working on a way to quantify the distance and speed a car would reach depending on its motor selection and the gear-ratio options.

The TT-01E gear-ratios were selected. Other chassis ratios would simply fit in-between.

Calculation assumptions:

  • Tire radius: 65 mm
  • Total vehicle weight: 2.0 Kg
  • Motor performance data taken from graphs found at the back of their Tamiya boxes. Silvercan (from Torque tuned motor box), Torque Tuned and Super Stock TZ
  • Zero wheelspin (all torque is transmitted to the ground)
  • Zero chassis losses (friction, etc)
  • Zero rolling resistance with ground
  • Zero wind resistance
  • Zero rotational inertia, which is the energy needed to spin drive-train elements. Only the intertia to move the car forward in a straight line was considered. This means that what loads the motor is the acceleration inertia.
  • No heat-related issues (e.g. overheating)
  • Battery current can keep up with power demand
  • Zero gear backlash
  • Flat surface (no incline)

Note that these assumptions mean the current calculation overestimates the car performance, given everything is considered as ideal, but at least it is a starting point to visualize general trends and as a foundation to build a more complex model.

Below the resuts:

1698312325_GearsSpeedvs.TimeKph.thumb.png.19c10bdbdc6526c0a81ccd5e63d9b05b.png

 

1183395490_GearsDistancevs.Time8m.thumb.png.785248ad8ff05134ab7a167bfe51699a.png

1696944246_GearsDistancevs.Time50m.thumb.png.49d824e88fdd18994db142c45a6aed43.png

You can see that in general shorter gear ratios will result in faster initial speeds, but eventually the longer ratios will catch-up and overtake them. The timing and distance of these cross-over points are the key takeaway from the grahps.

I plan to later correlate some of this information with the only real-life testing data I've been able to find on the web, which are  Cageman's videos you can find on Youtube, where different gear-ratios, motors, etc are tested and timed. For example:

The next step would be to either tweak the model to fit real-life test data and/or add modules that introduce calculations to correct previous assumptions. For example:

  • Chassis friction torque loss vs. rotational speed. This could me approximated by measuring motor current at different chassis free-wheel rpms on a bench. The current correlated to torque (using the motor perf graph) and then producing a torque loss vs. speed curve.
  • Wind resistance vs. speed. I guess a theoretical empirical calculation could be used as a function of body cross-section area.
  • Batter current output vs. motor current demand. Would have to see if battery info is available somewhere

Input/feedback/help welcome :) 

Edit: Changed units from m/s to Km/hr. Thanks @DeadMeat666for the suggestion!

Edit 2: Split distance vs. time graphs: 5sec and 1sec zoom. Added the assumption that heat-related issues are not considered.

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I take it you also assumed that heat is not a factor.

Very interesting study. The SuperStock is quite a jump up from the Torque Tuned, and I suppose the Sport Tuned would be somewhere in between the Torque Tuned and the SS.

Probably a good idea would be to multiply the m/s figures by 3.6 so that the speeds are displayed in km/h, which we can all relate to.

Great work!

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I think the results will get much more interesting once you add the data from a low-turn race motor.  The point with those is you must run lower* gearing, because they don't have the torque for high-speed gearing.  On a touring car track, a low-turn motor with low gearing will put in a faster laptime than a higher-turn torquey motor with higher gearing.  I don't have huge experience with low-turn race motors, so I don't know if that "less torque low down" issue is genuinely a thing, or if it's actually the heat that's the problem.

In theory you could gear a low-turn motor with low gearing to have the same top speed as a high-turn motor with high gearing, but I've always assumed the low-turn motor would still beat it on track, otherwise everybody would run cheaper high-turn motors that draw less current and produce less heat.

*at some point we'll have to decide what constitutes "low" and "high" gearing, which is a concept I've got confused with before.  I've always used "low" to refer to low speed, high-acceleration gearing (probably from the automotive world where we say "use low gear for hills" or the agricultural world where we say "use low range for towing equipment") but I've heard others use "low" to refer to the ratio, i.e. 5.72 is lower than 8.35 but has a higher top speed.

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You've put a lot of effort into this but you already know that it is complete nonsense. "Theroetical" isn't even a fair description of a no load situation. Someone is going to come along, read this thread, put the biggest pinion they can find on a Super Stock motor, and then be shocked when it overheats.

Making your car fast is pretty straightforward. More power = more speed. Gear them appropriately for the environment you are running in, and watch the temperatures so you don't cook them.

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2 hours ago, DeadMeat666 said:

Probably a good idea would be to multiply the m/s figures by 3.6 so that the speeds are displayed in km/h, which we can all relate to.

Done, thanks for the input! :)

2 hours ago, sosidge said:

You've put a lot of effort into this but you already know that it is complete nonsense. "Theroetical" isn't even a fair description of a no load situation. Someone is going to come along, read this thread, put the biggest pinion they can find on a Super Stock motor, and then be shocked when it overheats.

Making your car fast is pretty straightforward. More power = more speed. Gear them appropriately for the environment you are running in, and watch the temperatures so you don't cook them.

I think you are missing the point. Theoretical in this case means an upper limit and I find it quite useful. I'm sorry you find it is complete nonsense, perhaps you need to understand the benefit of the data. More power does not necesarily always mean more speed. For example, the graphs show:

  • Consider a Torque Tuned at 5.72 ratio vs a Super Stock TZ at 8.35 ratio. Note the Super Stock TZ has far more power than the Torque Tuned.
  • If you are interested in acceleration, see the expanded distance graph included below. Accelerating from a stand-still, the Super Stock TZ with 8.35 ratio will lead for the first 24m stretch (2.1m lead at best at around 1.25 seconds), after which the Torque Tuned with 5.72 ratio will overtake it. After 5 seconds, the Torque Tuned will have a 3 meter lead.
  • If you are interested only in top-speed, then the Torque Tuned at 5.72 will be best (39.7 vs 34.7 Km/h).
  • On both the above motor & ratio scenarios, temperatures can be easily managed using a heatsink + fan, or even just a heatsink if you are in a reasonably cool place.

1747720051_GearsDistancevs.Time50m.thumb.png.c4882614a74f0c51663d90fa819cb3e3.png

The charts give you the information needed to see where the cross-over points between motors and ratios are. You can then make an informed decision on what gear ratio to choose depending on what your objective is, what equipment you have on hand and what heat management solution is needed.

Having said that, perhaps another module that can be introduced into the model could be including motor efficiency which can tell you energy consumption vs travelled distance (or a number acceleration/stop cycles). This could be useful in anticipating heat and battery consumption.

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2 hours ago, Mad Ax said:

In theory you could gear a low-turn motor with low gearing to have the same top speed as a high-turn motor with high gearing, but I've always assumed the low-turn motor would still beat it on track, otherwise everybody would run cheaper high-turn motors that draw less current and produce less heat.

This is one part about gearing I never understand. Go low turns, get all the RPM but waste it all on low gear due to lack of torque. Go high turns, get all the torque and able to go high gear and have the same speed as a low turns. (or is it the other way round? 😵

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20 minutes ago, alvinlwh said:

This is one part about gearing I never understand. Go low turns, get all the RPM but waste it all on low gear due to lack of torque. Go high turns, get all the torque and able to go high gear and have the same speed as a low turns. (or is it the other way round? 😵

I could be wrong here but I think it has to do with the ability of thicker wire to put more current through -the lower-turn motors have thicker wire than their higher-turn counterparts. For the fixed input voltage, the thicker wire results in less resistance given its larger cross-section and shorter winding length, thus allowing more current to go through.

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2 hours ago, DeadMeat666 said:

Probably a good idea would be to multiply the m/s figures by 3.6 so that the speeds are displayed in km/h, which we can all relate 

Surely , MPH?.......🙄🤣

 

11 minutes ago, alvinlwh said:

This is one part about gearing I never understand. Go low turns, get all the RPM but waste it all on low gear due to lack of torque. Go high turns, get all the torque and able to go high gear and have the same speed as a low turns. (or is it the other way round? 😵

Gearing isn't really an issue in modern day racing, it was big thing back in the brushed and Nicad days, when you picked your motor and gearing, to get the best performance, but it lasted a whole race. It was all to do with current draw, a low turn motor geared low ,may pull less amps ,than a high turn motor geared tall, and be more responsive out if the corners, meaning a quicker lap time.

With modern lipos and brushless , it's not really considered, they provide enough grunt for most conservative gearing, and you just add more turbo timing ,if you need more speed down the straight. 

2 hours ago, sosidge said:

You've put a lot of effort into this but you already know that it is complete nonsense.

Be interesting to see how accurate the 'box data' is in the real world, even under no load, we all know how much companies love to ,promote (?) ,their figures! 

I'll try and find it, but I'm sure ,Radio Race Car did a test in the 80's, using a aeroplane propeller to add load, and an optical sensor to measure the rpm. 

 

50 minutes ago, OoALEJOoO said:

I think you are missing the point

Great work, collecting all the manufactures data, into one handy graph, are you planning on bench testing any motors to confirm data? 

All I can add, is when I wanted to go quicker, I went brushless....

 

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39 minutes ago, OoALEJOoO said:

I could be wrong here but I think it has to do with the ability of thicker wire to put more current through -the lower-turn motors have thicker wire than their higher-turn counterparts. For the fixed input voltage, the thicker wire results in less resistance given its larger cross-section and shorter winding length, thus allowing more current to go through.

Gosh, you just made it worse. I have not gotten my head around gearing yet and you are introducing current and guage into the mix. 😅

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1 minute ago, Wooders28 said:

Gearing isn't really an issue in modern day racing, it was big thing back in the brushed and Nicad days, when you picked your motor and gearing, to get the best performance, but it lasted a whole race. It was all to do with current draw, a low turn motor geared low ,may pull less amps ,than a high turn motor geared tall, and be more responsive out if the corners, meaning a quicker lap time.

With modern lipos and brushless , it's not really considered, they provide enough grunt for most conservative gearing, and you just add more turbo timing ,if you need more speed down the straight. 

So I guess it still is an issue for me since I run brushed and mostly NiMHs. 

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Physics question, with zero resistance in your model, what stops the cars from accelerating indefinitely?

Or is it the coupling of the wheel to the motor with a fixed RPM?

 

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On 9/26/2021 at 7:48 PM, Nikko85 said:

Physics question, with zero resistance in your model, what stops the cars from accelerating indefinitely?

Or is it the coupling of the wheel to the motor with a fixed RPM?

The model does have load, which is the inertia to accelerate the mass of the car. A mass of 2.0 kg was used for this effect. I did made the assumption of no rotational inertia (i.e. the energy needed to spin all the elements of the drive train, besides them accelerating forward, perhaps something to include later, would need to weigh & measure every bit!).

What stops the car from accelerating indefenitely is the fact that the motors do not develop torque idefinitely. Their torque reaches a zero value after certain rpm, thus zero acceleration.

Edit: Adding a friction & air resistance module would reduce final max-speed. Right now the model neglects them, resulting in max-speed at the point where the motor torque is zero (since losses are deemed zero). In reality, max-speed would be the point at where available motor tractive force equals all speed-related losses, and acceleration where available motor tractive force exceeds all speed-related losses.

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2 hours ago, Wooders28 said:

Be interesting to see how accurate the 'box data' is in the real world, even under no load, we all know how much companies love to ,promote (?) ,their figures! 

I'll try and find it, but I'm sure ,Radio Race Car did a test in the 80's, using a aeroplane propeller to add load, and an optical sensor to measure the rpm. 

Great work, collecting all the manufactures data, into one handy graph, are you planning on bench testing any motors to confirm data? 

All I can add, is when I wanted to go quicker, I went brushless....

I've been wondering the same thing. I suspect the graph on the boxes shows calculated or approximated values, as opposed to real data, possibly with the added marketing sugar-coat ;)

Unfortunately I'm stuck with brushed + NiMh and no means for the needed test gear for a proper bench-test. A self-imposed limitation to keep hobby spending under control and prevent an entry on the following thread (although I think it's too late :) ):

https://www.tamiyaclub.com/forum/index.php?/topic/99555-think-i-have-a-problem-well-the-wife-does-anyway/

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10 minutes ago, OoALEJOoO said:

Unfortunately I'm stuck with brushed + NiMh and no means for the needed test gear for a proper bench-test. 

It appears that a laser RPM meter don't actually costs that much, so if you are really into finding out...

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15 minutes ago, alvinlwh said:

It appears that a laser RPM meter don't actually costs that much, so if you are really into finding out...

I was thinking about recording the sound the geartrain makes and then process the sound file using a FFT analyzer, assuming I can find the software for free online and my cell-phone is up to the task. The FFT should then break-down the spectrum into the frequencies the different ratios the drive-train is spinning. You'll get a spike at motor rpm, a lower one on spur rpm, and so forth until the lowest spike should be at wheel rpm. You might get some extra spikes at spur teeth count (rpm x # of teeth), and other multipliers, which would require some time identifying what is what. In theory it should be doable. Right now I think the most serious limiting resource is free time :(

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8 hours ago, sosidge said:

You've put a lot of effort into this but you already know that it is complete nonsense. "Theroetical" isn't even a fair description of a no load situation. Someone is going to come along, read this thread, put the biggest pinion they can find on a Super Stock motor, and then be shocked when it overheats.

Making your car fast is pretty straightforward. More power = more speed. Gear them appropriately for the environment you are running in, and watch the temperatures so you don't cook them.

Easy there, I was about to post the same thing this am (in a gentler tone), but I didn’t.   But I guess I just did.  :lol:  Haha

I think the point is it is fun thinking about these things and we welcome it.   Back in my racing days it was all about trial and error x10000 because besides gear ratio and battery, chassis weight, etc, everything else was too variable.  

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2 hours ago, OoALEJOoO said:

Adding a friction & air resistance module would reduce final max-speed. Right now the model neglects them, resulting in max-speed at the point where the motor torque is zero (since losses are deemed zero). In reality, max-speed would be the point at where available motor tractive force equals all speed-related losses, and acceleration where available motor tractive force exceeds all speed-related losses.

That's not all it would do. It would also reduce speed all along the curve, because acceleration, as you say, depends on the amount by which the tractive force exceeds the speed-related losses. With unmodelled losses all along the curve, the taller gear ratios, which provide less torque at the wheel than shorter ones, so will have less excess tractive force than shorter ratios, therefore are shown in a much more optimistic light than would be the case in reality. 

I'm other words, the unmodelled speed-related losses will disproportionately affect the taller gear ratios, so your graphs would look very different with them included in the model, and not just a shift downward for all ratios equally.  

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8 hours ago, Mad Ax said:

at some point we'll have to decide what constitutes "low" and "high" gearing, which is a concept I've got confused with before.  I've always used "low" to refer to low speed, high-acceleration gearing (probably from the automotive world where we say "use low gear for hills" or the agricultural world where we say "use low range for towing equipment") but I've heard others use "low" to refer to the ratio, i.e. 5.72 is lower than 8.35 but has a higher top speed

There are two ratios that people often conflate: gear ratio and speed ratio.

Generally people say gear ratio but they actually mean speed ratio. So a 7:1 ratio like a typical rc car means the pinion is spinning 7 times for every one rotation at the wheels. 

As a gear ratio, this would be 1:7. 

Confusingly, it is also possible (though not in a typical rc car) to have a 7:1 gear ratio, i.e., 7 times more teeth on the driving gear than on the driven one. So which is the 'higher' ratio - 1:7 or 7:1? 

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2 hours ago, OoALEJOoO said:

I was thinking about recording the sound the geartrain makes and then process the sound file using a FFT analyzer, assuming I can find the software for free online and my cell-phone is up to the task. 

I use this app for my Mini 4WDs. I cannot say how accurate it is though. 

https://play.google.com/store/apps/details?id=jp.nas.giri

 

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7 hours ago, OoALEJOoO said:

The model does have load, which is the inertia to linearly accelerate the mass of the car. A mass of 2.0 kg was used for this effect. I did made the assumption of no rotational inertia (i.e. the energy needed to spin all the elements of the drive train, besides them accelerating linearly, perhaps something to include later, would need to weigh & measure every bit!).

What stops the car from accelerating indefenitely is the fact that the motors do not develop torque idefinitely. Their torque reaches a zero value after certain rpm, thus zero acceleration.

Edit: Adding a friction & air resistance module would reduce final max-speed. Right now the model neglects them, resulting in max-speed at the point where the motor torque is zero (since losses are deemed zero). In reality, max-speed would be the point at where available motor tractive force equals all speed-related losses, and acceleration where available motor tractive force exceeds all speed-related losses.

This is what I was missing, thanks! I'm happy enough with Newtons laws of motion - and the post edit but couldn't understand why you're model didn't have them accelerate for ever. 

 

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3 hours ago, OoALEJOoO said:

I was thinking about recording the sound the geartrain makes and then process the sound file using a FFT analyzer, assuming I can find the software for free online and my cell-phone is up to the task.

There's us spending thousands with Pruftechnik and IFM, and it's free online 😳

3 hours ago, OoALEJOoO said:

I think the most serious limiting resource is free time

Indeed, which is why I just throw a brushless and lipo in 😁

Although, I've been known to over gear those on speed runs, resulting in a slower mph...🤔

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I am interested in brushless motors factors. As some 4300kv motors perform differently from one another. I have a good quality turnigy 4300kv motor that out performs cheaper 5600kv speed motors. Yet my Vampire Racing mod spec motor which is apparently rated at 4300rpm is much faster and appears to have alot more torque, than both and I can run lower gearing meaning more top speed. 

Again in comparison my Vampire Racing AB+ 4.5T motor with my esc in 4300kv spec mode, is just below my spec motor in power and torque, but above my Turnigy motor.

I used to love brushed motors and tinkering with springs and brushes etc. But the 'new' (in 2003) brushless motors etc are just awesome. 👍 Sorry but nostalgia or not I certainly won't be going back to anything brushed any time soon., Heck the revolution started over 15 years ago 👍.

James.

James.

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3 hours ago, InsaneJim69 said:

As some 4300kv motors perform differently from one another. I have a good quality turnigy 4300kv motor that out performs cheaper 5600kv speed motors.

Pretty similar with brushed motors too though. A 15t firebolt won't perform the same as a Reedy Mr B's (15t) motor. Magnet strength, bearings etc.

With brushless, quality of magnets etc still effects performance (torque), but also, because sensorless are measured in KV, it doesn't tell you the full story. Some are 380 motors in a 540 size can (the 'finned' motors, like the Skyrc Leopard ) so the rpm is there but not much in the way of power (torque), my Castle 3800kv is night and day more powerful than my Goolrc 4300kv. 

If you judged a IC car engines power, on rpm alone, would you go for a 15,000rpm engine or a 9000rpm engine? You'd think the 15,000 would be quicker? 

The 15,000 is a chain saw making 3hp, the 9,000 is a Top Fuel Dragster engine making 11,000hp.....

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9 hours ago, rich_f said:

That's not all it would do. It would also reduce speed all along the curve, because acceleration, as you say, depends on the amount by which the tractive force exceeds the speed-related losses. With unmodelled losses all along the curve, the taller gear ratios, which provide less torque at the wheel than shorter ones, so will have less excess tractive force than shorter ratios, therefore are shown in a much more optimistic light than would be the case in reality. 

I'm other words, the unmodelled speed-related losses will disproportionately affect the taller gear ratios, so your graphs would look very different with them included in the model, and not just a shift downward for all ratios equally.  

Correct,  speed-realted losses indeed will affect the entire curve. Many of them are exponential with speed and therefore incurr heavier movement penalties the faster you go. The good thing is that qualitatively the trends on the graph would still be maintained (i.e. every ratio will be affected by speed, and not inherently by ratio). What could change, although I suspect not dramatically, might be the position of cross-over points.

8 hours ago, alvinlwh said:

I use this app for my Mini 4WDs. I cannot say how accurate it is though. 

https://play.google.com/store/apps/details?id=jp.nas.giri

Thanks! Will take a look.

Some thoughts on the modules that could make the model more accurate:

  • Chassis friction losses: Measure power consumption and speed at different speeds (varied via transmitter throttle). The output would be a delivered torque vs speed curve. Since the power measurement would be consumed power (as apposed to delivered power) it would have to be translated into delivered power using motor efficiency.
  • Wind losses: The starting point would be to pick a drag coefficient. I haven't really given it much though but perhaps choosing a real-car coefficient might work (?). Then use the basic equation of Drag Force = 0.5* air density * velocity ^2 * drag coefficient * body cross-section area. Depending on how it looks it might trigger further tweaking.
  • Battery output current: From Cageman's videos it is clear that a NiMh battery cannot supply enough current during initial acceleration (a LiPo will produce more acceleration). However, the NiMh does produce the same max-speed as a LiPo. This makes sense given motor power consumption goes down as RPM go up. Having data on NiMh max current output could be used to introduce a limit on available power (torque).
  • Rotational inertia: measure the diameter and mass of every rotating element and calculate its moment of inertia. The module would then add rotational inertia build-up alongside the linear inertia.

You can see that while the theoretical model applies to a broad range of chassis (except for the mass and tire diameter, which are simple inputs), the modules would be chassis, body and equipment specific (yikes!).

Making the theoretical model required a relatively smaller effort, at the end of the day it was a fairly straightforward MS Excel job. The bulk of the work will be making the add-on modules that address assumptions - this is the real time-sink :)

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