# Gear ratios for this motorcycle

• i_am_imbact
In summary, the conversation discusses using a polynomial function to determine the speed at which gears should be changed in a motorcycle engine with known transmission ratios. The speaker also mentions trying to solve a first differential equation using MATLAB, but does not specify what they are trying to solve for. Another participant suggests using a graph to find the intersection point of adjacent gear curves to determine the shift point. The conversation ends with a discussion about the influence of gear ratios on highway cruising speed.
i_am_imbact
Hello guys

I have a motorcycle engine in which I know the ratios of the transmission. and given the diagram of Power and rpm I made a function of P(ω) which is a polynomial of 6 order.

Then I said that F(friction)*u=P(ω) then I substitute ω=u*r/v v(ratio) and have F(u).Next knowing the Pmax and the ratios I found the speed in which we should change the gear 1st to 2nd and etc (Fu=Pmax) and in the end I have 5 equation of F (5 gears in the transmission).

In the end I tried to solve the first differential for the first gear (Fu-1/2*b*cd*u^2=m*du/dt) but there is no solution(tried to solve it with matlab).Do you know what I have to change or where I did a mistake in order to solve my problem?

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Maybe see if this website helps with your problem. It's looking at shift points from a practical point of view, using dynomometer measurements to back it all up. Maybe it will give you some insights into the way that you want to try to do this with calculations...

https://www.evodynamics.com/blogs/news/114447365-calculating-shift-points

FactChecker and Tom.G
From that nice graph that @berkeman found, it looks like the shift point is at or just before the intersection of the curves for adjacent gears.

Given that, subtract the equations of two adjacent gears and solve to find where they intersect.
f (1stGear) - f (2ndGear) = 0

Cheers,
Tom

FactChecker
i_am_imbact said:
In the end I tried to solve the first differential for the first gear (Fu-1/2*b*cd*u^2=m*du/dt) but there is no solution(tried to solve it with matlab).
A solution for what unknown? What is it you want to find?

From what I understand (I assume you mean F(u) not Fu), you know F (which is a function of u) and you know b, cd & m. You then have a function of du/dt with respect to u. Knowing your velocity, you know your acceleration.

Welcome to PF.
If you have equations for 5 gears you can solve for the 4 equal power points for the gear changes.
I think you need to explain what you are trying to solve for.
It is often the case that clearly explaining the problem finds the answer.

Tom.G said:
From that nice graph that @berkeman found, it looks like the shift point is at or just before the intersection of the curves for adjacent gears.

Given that, subtract the equations of two adjacent gears and solve to find where they intersect.
f (1stGear) - f (2ndGear) = 0
The OP does not specify how the gear ratios were determined. From the example graph, it looks as though the shift point might be the RPM redline, which might be before the torque curves intersect. I suspect that will be true for any well-designed transmission gear ratios. Certainly that is true for the low gears of any motorcycle that I have ridden. I guess that the design of the upper gear ratios might be influenced by the typical highway cruising speed.

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## 1. What is a gear ratio?

A gear ratio is a numerical expression that represents the relationship between the number of teeth on two gears that are meshed or connected in a mechanical system. In the context of motorcycles, it refers to the ratio between the number of teeth on the front sprocket (connected to the engine) and the rear sprocket (connected to the wheel).

## 2. How does gear ratio affect a motorcycle's performance?

The gear ratio directly affects a motorcycle's acceleration, top speed, and fuel efficiency. A lower gear ratio (smaller front sprocket or larger rear sprocket) provides more torque and quicker acceleration, but lower top speed. On the other hand, a higher gear ratio (larger front sprocket or smaller rear sprocket) results in less torque and slower acceleration, but higher top speed and better fuel efficiency.

## 3. What is the ideal gear ratio for my motorcycle?

The ideal gear ratio for a motorcycle depends on various factors such as the engine power, weight of the motorcycle, and intended use. Generally, a lower gear ratio is preferred for off-road or city riding, while a higher gear ratio is more suitable for highway riding. It is best to consult your motorcycle's manufacturer or a mechanic for the recommended gear ratio for your specific bike.

## 4. How can I change the gear ratio on my motorcycle?

The gear ratio on a motorcycle can be changed by replacing the front and/or rear sprockets with ones that have a different number of teeth. This can be done by a professional mechanic or by yourself if you have the necessary tools and knowledge. However, it is important to note that changing the gear ratio can affect the overall performance and may require adjustments to the chain length and tension.

## 5. Can changing the gear ratio damage my motorcycle?

Changing the gear ratio on a motorcycle can potentially damage the engine if the new ratio is too extreme for the bike's capabilities. It can also put excess strain on the chain and other components, leading to premature wear and tear. It is important to carefully consider the potential effects and consult a professional before making any changes to the gear ratio of your motorcycle.

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