# What Gear Ratio Is Needed for a 30-40 km/h Electric Longboard?

• Automotive
• Gurfin321
In summary: The power required to go 15 km/h (= 4.17 m/s) on a 10° incline:\begin{split}P &= 0.5\rho C_D A v^3 + (mg\sin\theta) v \\P &= 0.5 (1.225) (1.00) (0.9) (4.17)^3 + ((65)(9.81)\sin(10)) (4.17) \\P &= 502\ W
Gurfin321
I would like to know what gear ratio i would need for my electric longboard. The goal is to run the longboard at 30 - 40 km/h at max power. Me and the longboards weight is approximately 65 kg. The brushless motor i am running has an rpm of approximately 18000 rpm (as it is an airplane engine) and a torque of 1,24 Nm. I would like to be able to go up a 10 degrees incline at 10 - 20 km/h. The longboard wheel is 75 mm in diameter. My question to you is: "How big a gear ratio should i use, and achieve said goals?". I would like to know all formels and equations, and also all the variables.

//Josef

Gurfin321 said:
I would like to know what gear ratio i would need for my electric longboard. The goal is to run the longboard at 30 - 40 km/h at max power. Me and the longboards weight is approximately 65 kg. The brushless motor i am running has an rpm of approximately 18000 rpm (as it is an airplane engine) and a torque of 1,24 Nm. I would like to be able to go up a 10 degrees incline at 10 - 20 km/h. The longboard wheel is 75 mm in diameter. My question to you is: "How big a gear ratio should i use, and achieve said goals?". I would like to know all formels and equations, and also all the variables.

//Josef
Welcome to the PF.

Is that the kind of electric motor that is routinely used in commercial battery-powered longboards? Such a high RPM motor (which is useful for RC aircraft would seem to be not well suited to a lower-RPM higher-torque application like a longboard.

berkeman said:
Welcome to the PF.

Is that the kind of electric motor that is routinely used in commercial battery-powered longboards? Such a high RPM motor (which is useful for RC aircraft would seem to be not well suited to a lower-RPM higher-torque application like a longboard.
No it is not, however i can if needed switch motor, as long as it will suit my needs, budget is not a grate problem. I would like to get it as cheap as possible, while stil remaining top quality.

Gurfin321 said:
No it is not, however i can if needed switch motor, as long as it will suit my needs, budget is not a grate problem. I would like to get it as cheap as possible, while stil remaining top quality.
From an engineering perspective, the losses in such a high gear ratio will cost you power and battery life. It would be much better to find out what type of motor is used on commercial longboards, and see how inexpensively you can buy one (like on eBay or similar). Do you have access to a commercial battery-powered longboard that you can check the motor type/brand/size? If not, I have a good friend who commutes to Stanford on his battery-powered longboard. I could ask him...

berkeman said:
From an engineering perspective, the losses in such a high gear ratio will cost you power and battery life. It would be much better to find out what type of motor is used on commercial longboards, and see how inexpensively you can find one (like on eBay or similar). Do you have access to a commercial battery-powered longboard that you can check the motor type/brand/size? If not, I have a good friend who commutes to Stanford on his battery-powered longboard. I could ask him...
I do not have access to an electric longboard, so it would be greatly appreciated if you could ask him for advise. Thanks!

Will do.

Here is his reply. Can you follow up on the Internet info about the board and motor?

I'm in the Idaho backcountry biking between hot springs . My board is a Boosted Dual Plus. Not sure whose motor they are using, but there is a teardown on the net so you can find it. Battery is 99 Watt-Hours.

Cheers

berkeman said:
Here is his reply. Can you follow up on the Internet info about the board and motor?
I was not able to find boosted motor however, on some other longboard diys they used motor like these http://www.hobbyking.com/hobbyking/...sk3_5055_280kv_brushless_outrunner_motor.html
While my motor should be even more powerful! (Sorry swedish site) http://www.hobbex.se/sv/artiklar/rimfire-80-50-55-500-borstlos-elmotor.htmlWill it work?

Quick analysis:

Possible top speed ##v_{max}## in (m/s):
$$v_{max} = \sqrt[3]{\frac{P_{max}}{0.5\rho C_DA}}$$
Where:
• ##P_{max}## = maximum motor power (2200 W, from your source);
• ##\rho## = air density (1.225 kg/m³);
• ##C_D## = drag coefficient (http://www.taylors.edu.my/EURECA/2014/downloads/02.pdf ##\approx## 1.00);
• ##A## = frontal area (standing human ##\approx## 0.9 m²).
This gives 15.86 m/s or about 57 km/h.

Power required to go 15 km/h (= 4.17 m/s) on a 10° incline:
$$\begin{split} P &= 0.5\rho C_D A v^3 + (mg\sin\theta) v \\ P &= 0.5 (1.225) (1.00) (0.9) (4.17)^3 + ((65)(9.81)\sin(10)) (4.17) \\ P &= 502\ W \end{split}$$
The gear ratio needed (assuming there is sufficient power at the motor rpm):
$$GR = \frac{rpm_m}{rpm_w} = \frac{\pi}{30}\frac{rpm_m r}{v}$$
Where:
• ##rpm_m## is the motor rpm (rpm);
• ##rpm_w## is the wheel rpm (rpm);
• ##v## is the speed (m/s);
• ##r## is the wheel radius (m).
Say you have a 70 mm wheel (= 0.035 m radius), then if you want to reach 40 km/h (= 11.1 m/s) when the motor is at 18 000 rpm, then you need a gear ratio of 5.94:1. But you may not need to reach that rpm since you have enough power to reach 57 km/h.

Of course, you need to make sure the motor can produce the required power at every speed (i.e. considering actual rpm motor at that speed), in every condition you expect (i.e. incline), with the gear ratio selected.

Last edited by a moderator:
berkeman and Gurfin321
jack action said:
Quick analysis:

Possible top speed ##v_{max}## in (m/s):
$$v_{max} = \sqrt[3]{\frac{P_{max}}{0.5\rho C_DA}}$$
Where:
• ##P_{max}## = maximum motor power (2200 W, from your source);
• ##\rho## = air density (1.225 kg/m³);
• ##C_D## = drag coefficient (http://www.taylors.edu.my/EURECA/2014/downloads/02.pdf ##\approx## 1.00);
• ##A## = frontal area (standing human ##\approx## 0.9 m²).
This gives 15.86 m/s or about 57 km/h.

Power required to go 15 km/h (= 4.17 m/s) on a 10° incline:
$$\begin{split} P &= 0.5\rho C_D A v^3 + (mg\sin\theta) v \\ P &= 0.5 (1.225) (1.00) (0.9) (4.17)^3 + ((65)(9.81)\sin(10)) (4.17) \\ P &= 502\ W \end{split}$$
The gear ratio needed (assuming there is sufficient power at the motor rpm):
$$GR = \frac{rpm_m}{rpm_w} = \frac{\pi}{30}\frac{rpm_m r}{v}$$
Where:
• ##rpm_m## is the motor rpm (rpm);
• ##rpm_w## is the wheel rpm (rpm);
• ##v## is the speed (m/s);
• ##r## is the wheel radius (m).
Say you have a 70 mm wheel (= 0.035 m radius), then if you want to reach 40 km/h (= 11.1 m/s) when the motor is at 18 000 rpm, then you need a gear ratio of 5.94:1. But you may not need to reach that rpm since you have enough power to reach 57 km/h.

Of course, you need to make sure the motor can produce the required power at every speed (i.e. considering actual rpm motor at that speed), in every condition you expect (i.e. incline), with the gear ratio selected.
THANK you! Great help, really got stuck with this one.

Where did you learn all this, i would like to know the source as it might come in handy to solve other practical problems.
Now me and my buddy are going to build an awesome longboard.
Again Thanks!

//Josef

bellesbarbara, bsheikho and Gurfin321

## 1. What is gear ratio and why is it important in electric longboards?

Gear ratio refers to the ratio of the number of teeth on the larger gear (driven gear) to the number of teeth on the smaller gear (driving gear). In electric longboards, gear ratio is important because it determines the speed and torque of the board. A higher gear ratio will result in a faster but less torquey ride, while a lower gear ratio will provide more torque but a slower speed.

## 2. How do I calculate the gear ratio for my electric longboard?

To calculate the gear ratio of your electric longboard, you need to know the number of teeth on both the driving and driven gears. Then, divide the number of teeth on the driven gear by the number of teeth on the driving gear. For example, if the driven gear has 40 teeth and the driving gear has 20 teeth, the gear ratio would be 40/20 or 2:1.

## 3. What is a good gear ratio for an electric longboard?

The ideal gear ratio for an electric longboard will depend on your personal preferences and riding style. Generally, a gear ratio between 2:1 and 3:1 is considered a good range for most riders. However, if you are more interested in speed, a higher gear ratio of 3:1 or higher may be more suitable. If you prefer more torque and acceleration, a lower gear ratio of 2:1 or lower may be better.

## 4. Can I change the gear ratio on my electric longboard?

Yes, it is possible to change the gear ratio on your electric longboard. However, this will require purchasing new gears and possibly adjusting the motor mount to accommodate the new gear size. It is recommended to consult with a professional or experienced rider before attempting to change the gear ratio on your electric longboard.

## 5. How does gear ratio affect battery life on an electric longboard?

Gear ratio can have an impact on the battery life of an electric longboard. A higher gear ratio will result in a faster speed, but this also means the motor will be working harder and using more battery power. A lower gear ratio may provide more torque and a longer battery life, but at the expense of speed. It is important to find a balance between gear ratio and battery life that suits your riding style and needs.

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