Though this post is on the same day as the previos, these were written one or two weeks back.

My last article ends with me wondering how gear ratios are decided, and why it is in geometric progression.

After some discussions with my friends, I got the following inputs from a friends’ friend, who was working on it for some time.

The Gear ratios should be such that

1. During the shifting there should not be much change in acceleration.

2. It should be such that it brings the engine to lower SFC range for better fuel efficiency.

My friend was studying on optimizing gear ratios. He has given me some valuable inputs. The constraints, the parameters we should consider, etc. It is given below.

1. Minimum Gradability/restart gradability

2. 0-60kmph in 1900m.

Now MY Way of Designing (theoretical, hmmm can be called Philosophical also) and the Explanations…

I start with assumption that I have the engine, its Power, Torque Characteristics available.(I guess it should be available, I cant go around in dark).

Now I fix the maximum speed and based on it I can find approximately the maximum power losses (Definitely, This will be an approximate value). From the power curve, I will get the point corresponding to that, also the engine rpm. I already fixed the maximum speed and hence I can fix the final drive ratio.

The first gear ratio, I guess, as I have mentioned, will depend on the starting load. (For a sports car – not sure).

The Differential ratios along with the first gear ratio decide the Gradability/restart gradability of the Vehicle (Given an Engine – ).

Now the first and final gear ratios are fixed, I guess(Theoretically)

It is obvious that, the larger the no of gears we have, better will be the acceleration and the fuel economy, by letting the engine run at the Peak torque rpm/low SFC region

But the maximum no of gears, I guess will be limited by the size of the Gearbox (not good going for a large GB, obviously) and the moment of inertia of the rotating gears.(Larger the no. of gears in GB where gears are meshed all the time, larger the inertia, again obvious.) – I would like you to share with me your ideas and knowledge on deciding the no of Gears for a vehicle.

It also depend on the torque band in which we decide to work, I think. The torque band with gears should cover the entire speed range. (refer to the picture in the last post)

Now the no of gear ratios for Gearbox is fixed, say 5 or 6.

Considering the first two points – the acceleration while shifting gears should not change, and the working in lower SFC range.

- if the gear is shifted at the meeting point as shown in the graph, the acceleration is same.

- After we decide the optimum torque band, SFC band, the design should be such that the speed at the minimum rpm in the higher gear equal the speed at maximum rpm of lower gear. This will ensure the working in a particular rpm band. Which if strictly followed implies, the Geometric progression in the gear ratios is equal to the ratio of the maximum value of rpm to the minimum in the decided rpm band.

But we know, the gear ratios don’t follow geometric progression strictly, but with some variation. The variation to account for emission and some other properties – Again please give us your view/share your knowledge.

Following only torque and SFC, based on the band selected the passing gear ratios can be fixed.

Now to check theoretically if the vehicle can reach the 0-60 in 1900m.

We will assume proper shifting (shifting at the joining points).

From the force-velocity graph, we can get the acceleration-velocity graph.

(Acceleration on Y and Velocity on X axis)

Now, the displacement S = V x V/ 2 a. From basic kinematics equation

To find out the displacement, S = 0ƒ60 x/y .dx

The integral can be split into no of parts equal to the no of gears.

(This integration is a bit too much. Atleast for me, Hmmm OK, its theoretical)

Now some inputs from MY Friend R. Harish.

The decision of the gear ratios will depend on the ‘duty cycle’ of the gears. The duty cycle depends on whether we are using it in highway (constant speed at higher gears) or hilly/rough terrains (- where the driver never even know that 5th and 6th exist!)

Yeah – that’s practical, too practical for MY Explanations (you will never know where to stop explaining). He is into designing the gear ratios!

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## 1 comment:

Oh man what a detailed explanation ??

As usual alle ? hehe .

Gears are chosen in racing bikes so that the bike stays in powerband when the shift is made .

eg Power band of the engine starts from 5000 rpm to 7000 rpm .

The second gear ratio will be such that when the driver upshifts from first gear at around 7000 rpm , the rpm should not fall below 5000 rpm so that the bike is still in the powerband . Then there is close ratio gearbox for rallys and drags where the gear ratios are close by so that the driver remains in the power band throughout the race .

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