# What Gear Ratio Should I Use for Maximum Speed on My Model Car?

• 9988776655
In summary: The required torque from your axle is:Mo = mgL*9.8m/s/0.3kgMo = 0.1m*0.3kg*9.8m/sMo = Required torque = 0.294Nm
9988776655
Im building a model car with mass 0.3kg. I am thinking of buying a fancy 6 speed gearbox. But before I spend my money, I need to know if any of the gear ratios are going to move my little car.

Here is the motor:

the gearbox has ratios:
11.6:1
29.8:1
76.5:1
196.7:1
505.9:1
1300.9:1

If I wanted maximum speed, but I want my car to run, which gear ratio should I use?

I have four wheels, each 0.0028m in radius. I am using a 3V battery. The gearbox drives an axle which runs through two wheels. The torque applied by the axle is through the centre of rotation. The coefficient of rolling friction between the ground and the tire is about 0.01, maybe a bit less since the tires are so small.

I know that F = umg where u is the coefficient of friction but that's it. Please teach me how to work out a similar problem for next time. I have a feeling that I will be building a lot of model cars in the future.

I must admit that I'm a bit baffled by the question. The one serious advantage of an electric motor over an IC one is that you don't need a transmission.
Your ratios look way out of whack to me, as well. Are you trying to get this thing supersonic or pull stumps with it?

So any gear ratio will work? well my car is also remote controlled and it has steering which will be pretty impressive. Ill put a picture up when its done.

I don't see how they gear ratios are out of whak. All I want is a fast little car to race my friend's one. Here is the product specification:

http://www.tamiyausa.com/product/item.php?product-id=72005"

If my vehicle weighs 0.3kg and all the weight is in the middle and it is 0.2m long, the required torque from my axle is:

Mo = mgL
Mo = 0.1m*0.3kg*9.8m/s
Mo = Required torque = 0.294Nm

But I have 4 wheels but i don't know how this effects my torque calculation.

working torque = stall torque / 2 <------ should i rather use torque at maximum efficiency here as given in the motor spec in previous post?
= 0.00686N / 2
= 0.00843N

Gear ratio = required torque / working torque
Gear ratio = 0.294N / 0.00843N
= 34.9:1

But my spur gears arnt that efficient
Would this calculation be correct??

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I think that I see the difficulty here. (There are a lot of other people here who know far more about it, though, so don't take me at my word.) That gearbox appears to be intended for robotic applications, where you might need incredible torque increases over what the motor itself could provide directly.
Have you even considered checking the math to see how fast your little car would go with a 9,400 rpm motor geared down 1,300:1? As I said, it would be a stump-puller, except you wouldn't have any traction to make use of the torque. If you had the tranny installed backwards, as I originally thought that you meant, you wouldn't have enough torque to push a feather out of your way, but you'd have the sucker moving like greased bacon through a goose's ass once it managed to accelerate.

So it would go pretty swiftly but will it be able to accelerate with 1300:1?

This "R/C" car you're planning on building sounds like its WAY smaller than any standard racing R/C car I've ever heard of... we're talking even smaller than those little Zip-Zaps miniature R/C cars you can buy at Radio Shack. The tires are only 5.6mm in diameter?! This thing is going to be way smaller than that transmission by itself, and like Danger said, it doesn't look like it is made for a car application that is shift-on-the fly.

I the same vein, it sounds like that motor you have specced out doesn't have much power at all... 1/10th scale race-quality motors for competition typically put out at least 50-100times as much torque, and 50 times as much total power using up to a 7.2V battery; and they rev up to over 20,000rpm.

I would recommend browsing around www.towerhobbies.com for some ideas. They have lots of kits and race/hobbby specific products for R/C vehicles.

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they are 5.6cm diameter maybe i put the decimal point in the wrong place oops. I thought the motor had a bit more power than that. Maybe i need buy a more powerful gearbox/motor combination. I thought since my car was only 20cm long and weighs 300g all up a weak motor would be okey

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9988776655 said:
So it would go pretty swiftly but will it be able to accelerate with 1300:1?

That kind of reduction would give you an output shaft speed of only 5.8rpm, useless for anything that wants to go faster than a slug.

Even assuming direct drive to the axle after the transmission, 5.4rpm would equate to about 10cm/min. The "minimum" reduction in that transmission would equate to about 20cm/s (7 in/s); not very fast in my opinion, but maybe fast for such a small vehicle.

Again, it sounds to me like this "transmission" will be larger than the rest of your car combined.

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9988776655 said:
they are 5.4cm diameter maybe i put the decimal point in the wrong place oops. I thought the motor had a bit more power than that. Maybe i need buy a more powerful gearbox/motor combination

What kind of R/C racing are we talking about here? The real deal, or just for fun with home made stuff? How big is the car supposed to be?

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thats way too slow but at least it can accelerate. I tried to work it out before and I got that 34.9:1 would be a good ratio so I would pick the only one close to that 76.5:1 which the gearbox offers. Thats 100 rpm. Would that be able to drive the car or do you think I need a more powerful gearbox/motor? Its for fun. It can be whatever size but of course i need it big enough to fit a receiver pcb, batteries and the gearbox itself. I am using plywood as a chassis. I am in second year uni doing mechatronic engineering but all they teach me is programming, maths and statics. What is the use of that?

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9988776655 said:
thats way too slow but at least it can accelerate.

No, it can't. That's maximum linear speed with the motor running at its maximum speed with no load.

9988776655 said:
I tried to work it out before and I got that 34.9:1 would be a good ratio so I would pick the only one close to that 76.5:1 which the gearbox offers.

How did you choose that "good" ratio? Based solely on friction (which you have calculated incorrectly)? You're going to want a motor and gear combo that gives you WAY more power and torque than would be required to overcome friction, so that your car actually accelerates and can maintain a top speed.

9988776655 said:
Thats 100 rpm.

That's 2.9 cm/s based on the numbers you've posted thus far. Slow. Real slow.

9988776655 said:
Would that be able to drive the car or do you think I need a more powerful gearbox/motor? Its for fun. It can be whatever size but of course i need it big enough to fit a receiver pcb, batteries and the gearbox itself. I am using plywood as a chassis. I am in second year uni doing mechatronic engineering but all they teach me is programming, maths and statics. What is the use of that? My uni friends are having a race day in a few months

There's no way you're gonig to keep your vehicle weight under 0.3kg including batteries and electronics while building the vehicle out of plywood. I would guess at least triple that weight depending on overall size.

It sounds to me like your estimates and calculated numbers are all WAY off right now. My recommendation is to look at some cars that already exist, at a hobby shop for example, to get an idea of what size you're looking for, what driveline components you'll want, and how you plan to accomplish it.

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I feel a little hopeless after your post

My wheel is 5.6cm diameter, circumference 17.6cm.
My revolutions per minute is 100
My revolutions per second is 1.67
Every revolution, My wheel turns 17.6cm
My distance per second is 1.67r/s * 17.6cm = 29.5cm/s
But you got 2.9 cm/s? am i missing something?

You are right about my estimates being way off. It would me nice to actually know how to do the "torque required" calculation correctly but I don't know how.
I can't find a more powerful gearbox/motor combo

Im looking at another gearbox which may be just as bad. You can do
1:125
Does that mean for every 1 motor revolution, the axle turns 125 times?

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9988776655 said:
You can do
1:125
Does that mean for every 1 motor revolution, the axle turns 125 times?

Yes. So figure what that means with your 9,400 rpm motor.

I think ill pass on that gearbox then. I don't think 29cm/s is slow. But maybe i didnt work it out properly. To overcome friction initially I need:

torque > Us*m*g
torque > 0.4*0.5kg*9.8m/s
torque > 1.96N

(I used an estimate for the friction of rubber on wood)
Rolling friction has to be less than this
But I have 4 wheels so I don't know how that effects friction

Even with the highest reduction, my gearbox/motor still won't even move

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9988776655 said:
I feel a little hopeless after your post

No need to feel hopeless, we are here to help. I suspect you'll be able to build a very capable vehicle once we get a few basics ironed out.

9988776655 said:
My wheel is 5.6cm diameter, circumference 17.6cm.

Well there's the problem, your original post said the wheel radius was 2.8mm (0.0028m), so there was an extra zero in there.

9988776655 said:
You are right about my estimates being way off. It would me nice to actually know how to do the "torque required" calculation correctly but I don't know how.
I can't find a more powerful gearbox/motor combo

Well, I think your problem is that you're not really grasping what the friction calculation is useful for.

What you want is this thing to be fast, so you're going to want to accelerate at a decent rate, which means the majority of your motor's power will go towards accelerating the vehicle's mass. As long as all of the parts are chosen properly, friction should be a negligeble effect when compared to the required acceleration force.

9988776655 said:
Im looking at another gearbox which may be just as bad. You can do
1:125
Does that mean for every 1 motor revolution, the axle turns 125 times?

That is the reverse of what you would use a gearbox for. Since you're going to be using a small, fast-revving motor, the gearbox needs to be used to REDUCE the rotational speed, not increase it. So if you were using a gearbox with a 1:125 ratio, the output shaft of the gearbox will turn once for every 125 turns of the motor.

Are you going to be using a differential for the drive wheels, or will the output of the gearbox directly drive the rear wheels?

9988776655 said:
I think ill pass on that gearbox then. I don't think 29cm/s is slow.

It's all a matter of perspective. I have a "stock class" 1/10 scale electric off-road race buggy that easily goes 25 mi/hr, which works out to about 11 m/s (1100 cm/s). A 1/8th scale nitro-powered monster truck I have can hit a top speed of about 40 mi/hr (17 m/s, 1700 cm/s), even faster with different gearing.

9988776655 said:
But maybe i didnt work it out properly. To overcome friction initially I need:

torque > Us*m*g
torque > 0.4*0.5kg*9.8m/s
torque > 1.96N

(I used an estimate for the friction of rubber on wood)
Rolling friction has to be less than this
But I have 4 wheels so I don't know how that effects friction

Even with the highest reduction, my gearbox/motor still won't even move

YOU'RE NOT CALCULATING THE RIGHT KIND OF FRICTION. Static friction (what the above calculation you did is for) would be if the wheels were locked up, not rolling, and you were dragging the vehicle along the ground.

For your purposes, I would first assume friction to be negligible, and instead decide how fast you want your vehicle to accelerate to its final top speed. Then, using kinematics, you can figure out how much force would be required to accelerate it that quickly. From there, a motor can be chosen and a gear reduction can be decided on based on a required final top speed and acceleration.

To give you a better idea of what you should be looking for, start here:

http://www3.towerhobbies.com/listings/cat-c2.html

That is a basic listing of R/C car parts at tower hobbies, which should be very useful. They have tires, motors, bodies, controllers, servos, everything. In my opinion, it sounds to me like you wil want a "stock" 17 turn motor and regular speed controller, since they will be cheap, and far more powerful than the motor you currently have specced.

Motor Examples:
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXKCD0&P=0"
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXGKC7&P=0"

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Im thinking of using the gearbox that I was originally looking at but replacing the motor with of the ones you suggested. The gearbox is meant for a 2mm shaft but the 18-turn motor is 3mm. I do not know the diameter of the 17-turn motor. Do these motors also run on 3V?

The car is going to be on-road.

I thought to make the output shaft of the gearbox run the wheels.

I don't really need a speed controller. I am happy with max speed all time.

I worked out that the small components+wood+batteries+gearbox is 527g. If we change the motor it could be a bit heavier.

9988776655 said:
Im thinking of using the gearbox that I was originally looking at but replacing the motor with of the ones you suggested. The gearbox is meant for a 2mm shaft but the 18-turn motor is 3mm. I do not know the diameter of the 17-turn motor. Do these motors also run on 3V?

I don't think that gearbox will be a very good application for what you're trying to do. As said before, it looks to be more of an automation/robotics application for low speeds and forces.

While it's theoretically possible to run on 3V, why not just buy a single 6.4-7.2V battery pack? They're cheap, and specifically designed to work with the high current draw of this kind of motor.

Commonly the gear reduction used with these specific motors is a spur and pinion gear combination that drives a transaxle differential (combined transmission/differential), which in turn drives the wheels. Common pinion/spur ratios are around 1/3 to 1/4 (for example, a 78 tooth spur gear and a 24 tooth pinion gear, you can select different options to suit your driving style) and the transmission might be about 1/2.6, making the output speed to the wheels about 1/7 to 1/10 that of the motor's output speed. That setup (primarily off-road) would normally be used with 8.89 cm diameter drive tires, that are 6.1cm wide. On-road applications would be faster (less total gear reduction) with slightly smaller diameter tires.

9988776655 said:
I thought to make the output shaft of the gearbox run the wheels.

But how? You're going to need some sort of transaxle at very least to make the single output into dual axle shafts...

9988776655 said:
I don't really need a speed controller. I am happy with max speed all time.

Basic speed contrtollers are cheap, and these motors cannot be run without some sort of speed control. It is the throttle for the motor, so you can slow down in turns, and accelerate on straight aways. You have to remember it's going to have a pretty fast top speed and running with an on/off switch to the battery isn't really an option.

9988776655 said:
I worked out that the small components+wood+batteries+gearbox is 527g. If we change the motor it could be a bit heavier.

My guess without any calculation at all is you should aim for about double that, at least.

http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXBME7&P=7#otheritems

I also found these preassembled versions:
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXSXA9&P=7
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXLXX4&P=7

But I don't know what pinion gear to get to fit between the motor and the differention and I don't have housing for the differential. Why don't they include a pinion gear and housing set?

You're on the right track. Some R/C cars or trucks will have a transaxle that essentially houses the transmission and differential together, while other ones have separate differentials and transmissions.

It might be worth looking into parts for a Traxxas E-Maxx or T-Maxx, they have separate transmissions and differentials, and transmissions are available in single or dual speeds for the electric version of the truck.

The traxxas differentials have many parts to put together.
What do you think of this combination instead:

http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXSXA9&P=7
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXSWW1&P=Z
http://www3.towerhobbies.com/cgi-bin/wti0001p?&I=LXAMH5&P=Z

Do I need any other components? I can buy steel rods and a battery from another place cheaper and I have wheels already as well.

I hate to tell you now, but if you're looking to build a functioning R/C car, being afraid of putting a lot of parts together is probably not a good thing...

The motor you linked might be a little on the big side, but would still work (it's made for a monster truck it looks like). The differential "assembly" is the gear, bearings, and output shaft, but you will still need the entire transmission assembly and plastic housing that all of that goes in. you can't just drive the 'differential" directly with the motor, you need an interface between the two.

I would suggest looking up the exploded drawings of some stadium trucks or monster trucks such from companies such as Team Associated, Losi, or Traxxas (Traxxas has very easy to read drawings for our purposes). They are available free online, and will show you how the parts go together. For the Traxxas E-Maxx for example:

http://www.traxxas.com/products/electric/emaxx/trx_emaxx_views.htm#manual

You can see that it has a motor mount/transmission assembly that then has an output driveshaft that goes to the front and rear differentials (4WD). While it has the option for 4wd and two motors, it would be pretty easy to use just one motor with the transfer case, and then a single differential in the rear to put power to the ground. The nice thing about the Traxxas differential is it has it's own case, and can then be mounted where as the differentials you are finding go inside the case of the transmission/transaxle.

For an integrated transmission transaxle, you can see how it goes together on something like the Traxxas Rustler:

http://www.traxxas.com/products/electric/rustler/trx_rustler_views.htm#manual

Looking at the Rustler's Transmission assembly, you can see that the differential, motor mount, and "trasmission" are all combined into a single unit. So, if you bought a used (or new) complete Rustler transmission assembly, you would have everything you needed to put power to the ground on a rear wheel drive vehicle. All you need in addition to that would be a motor (and spur gear) and speed controller, and your radio receiver equipment. Then you would have to just try and mimic the truck's body mounts on the back that the transmission assembly mounts to.

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In addition to the off-road trucks I linked, which are designed with long axle shafts and big suspension travel in mind, Traxxas also makes some street vehicles, such as:

http://www.traxxas.com/products/electric/streetsport/trx_streetsport_views.htm#manual

You can see that the Street Sport is a sort of a NASCAR model that has a transmission very similar to the Statium truck, just smaller suspension travel. The street truck they make:

http://www.traxxas.com/products/electric/spirit/trx_spirit_views.htm#manual

The Spirit actually has NO suspension travel in the back because the entire transmission assembly pivots up and down, the wheels mount to the transmission directly. That might be one of the easiest integrations just because you don't necessarily need any shocks or suspension components.

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## 1. What factors should I consider when choosing a gearbox?

When choosing a gearbox, you should consider factors such as the load and torque requirements, speed and power requirements, mounting and installation requirements, and environmental conditions. It is also important to consider the type of application the gearbox will be used for, as this can impact the type of gearbox needed.

## 2. How do I determine the correct gear ratio for my application?

The gear ratio needed for your application will depend on the speed and torque requirements. To determine the gear ratio, you can divide the output speed by the input speed. For example, if your application requires an output speed of 500 rpm and the input speed is 1000 rpm, then the gear ratio would be 2:1.

## 3. What are the different types of gearboxes available?

There are several types of gearboxes available, including spur, helical, bevel, worm, and planetary gearboxes. Each type has its own unique features and advantages, so it is important to choose the one that best suits your application.

## 4. How do I know if I need a standard or custom gearbox?

If your application has specific requirements that cannot be met by a standard gearbox, you may need a custom gearbox. This could include special mounting or shaft configurations, different gear ratios, or specific torque or speed requirements. It is best to consult with a gearbox specialist to determine the best option for your application.

## 5. What is the typical lifespan of a gearbox?

The lifespan of a gearbox can vary depending on factors such as the quality of the gearbox, the maintenance and care it receives, and the application it is used for. On average, a well-maintained gearbox can last between 10-15 years. However, heavy-duty applications may require more frequent maintenance and potentially have a shorter lifespan.

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