[vermasach]

Originally Posted by sudev

Guys I am mentioning true speed observation based on GPS with external antenna.
Smaller diameter will have smaller circumference but also better gearing. That's the toss up.

Not going with drastic change but one size smaller.

I think, with smaller tyres the Engine RPM doesn't change. There could be a speedo error because of tyre's diameter variance but that's a pseudo measure. The correct GPS reads will be the same.

However in the real world, the co-efficient of drag value is lesser for smaller tyres and hence should result in a marginal increase in real speed. How much exactly-we will need a Physics scholar to solve the problem for the community.

[Sutripta]

Originally Posted by arjab

Of late, we have seen changing the final drive achieves a good balance.

The Maruti van originally came with a pretty short final drive. Given the vehicles available to us at that time, could almost say was fun to drive in the hills! Then kitna deta hai struck, and the final drive was made taller. It wasn't the same anymore. And if anything I felt that in the hills fuel consumption increased.

Regards
Sutripta

[venkyhere]

Interesting discussion
Let me add my 2 cent ingredients to this interesting soup

Before we think about wheels with larger dia v/s wheels with smaller dia, lets go down one step lower and determine what is it that limits the top speed of a vehicle ? There are two candidates
a) Engine RPM
b) air drag (both pressure drag and surface drag contributions are lumped beautifully together by the car maker when he gives a certain drag coefficient number, say 0.3 or 0.28 or something like that) where the drag force is proportional to speed^2 , and hence the power expended on it will be proportional to speed^3.

We have gears in cars, which will effectively eliminate (a) as the limitation for top speed, so that revv-limiter is not hit when making a high speed run in the correct gear (whichever gear it is 4/5/6/7).

Also, we can intuitively say, without working any math, that the top speed of a car will be achieved when the engine is outputting max* BHP, or in a zone near max BHP point. This will happen somewhere close to the higher rpms, much before hitting the revv limiter rpms.

So now, it boils down to a condition where, (b) air drag, will be the real limitation on the top speed of a car.

Engine power = power to overcome air drag + mech losses + thermal losses.

Now lets try to bring in the variables we have at play (rpm and radius R of the wheel and the gear ratio N** selected by the driver or autogearbox).

Engine power = func1 (rpm)
air drag power = func2 (velocity^3) = func2 ( (rpm/N x 2.pi.R)^3 )
mech losses = func3 (rpm) , ignoring other variables
thermal losses = func4 (rpm), ignoring other variables

So we have the equation

func1(rpm) = func2((rpm/N x2.pi.R)^3)+func3(rpm)+func4(rpm)

where, we are trying to determine the max value of (rpm/N x2.pi.R), when func1(rpm) is somewhere near the max BHP point of the engine. This need not be the exact max BHP point in the dyno chart, but instinctively we know, it will hover somewhere around that point, just ahead or just behind.

As you can imagine, even if we assume the degree of the above equation is a power of 3 (ignoring higher power terms from func3 and func4), its a pretty complex thing to solve, even if we are given full freedom to choose N and R. Evidently, the key is the modelling of the functions func1/2/3/4 ; post which, this needs to be plugged into something like MatLab with various choices of N and R and then we will get the answer.

Hence, I think this is what needs to be done, to accurately predict what N and R will maximize the linear speed of the car while also maximizing the power output from the engine. Racing teams and landspeed records teams would have well solved this or something similar to this.

If you are still reading this, let me put a disclaimer that I am nowhere near a mech engineer, and am just crap-hooting in the dark, with high school physics. Nevertheless, hope this was of some use & carries the discussion forward.

* its always at max BHP point when the car is fastest, not at max torque point (some people have the wrong notion)
** N includes gear ratio and final drive ratio as well.

[McLaren Rulez]

Check the rpm at which you achieve your top speed Sudev (doesn't matter what gear).

If that rpm is less than the max rpm, a smaller tyre size will help. Otherwise no.

[chieftain]

Hey all,

Am I missing something?
At any given rpm, wouldn’t the centers of each wheel move at rw*, w being the angular velocity of the wheel assuming there is traction? And since the gear ratios are the same, the wheel’s angular velocity would be invariant for a constant rpm in a given gear? This would imply that the speed will be lower. That would be why the speedo needs to be recalibrated down, as it was initially set up with the assumption that the radius of the wheels is as per factory.

From my understanding of gear ratios it only involves rotation frequency and not the actual speed with respect to ground of any shaft or wheel so this is what makes sense to me, and the losses due to friction of various types are overcome by the engine (revs). Sorry if I am wrong.

*For those who are not familiar: note that for a wheel that is purely rolling (has traction), the point of contact with the ground is stationary at any given time, so it is (again, at any given time) as if it is rotating about the point of contact with the ground (at that given time). The center of the wheel is at a distance r (radius) from the point of contact, so the path it traces (at that given time) is a circle of radius r centered at the point of contact rather than at the center of the wheel which is not stationary here. This circle is being traced at an instantaneous rate of w (angle/time), so by the fact that the angle sub tended by an arc is the ratio of its length and radius, the velocity of the center of the wheel is rw.

Another way to understand it which is more conceptual/intuitive (and the way it is taught in school) is to consider it as a simultaneous rotation and translation of the wheel, but that explanation requires more backstory.

[smuniswami]

The physical quantity "speed" is nothing but the Distance covered over a period of Time. For the same RPM, the distance traveled by a smaller wheel will always be SMALLER than the distance traveled by a larger wheel over the same Time Period.
Hence, the SPEED will always be LESS with a smaller wheel compared to a larger wheel when all other influencing factors are kept same.
However, one may attain the top speed quickly with a smaller wheel than with a larger one, provided the Torque is SAME in both cases.

[sudev]

Thanks a bunch guys. Interesting discussion all around.

Will share some pictures from test run. Need safe and open area to do so and thus not possible around Delhi. Have to go pretty far to do this.

[sudev]

Nearest example I can come up with is speed of Rajdoot motorcycle vis Bobby. Same engine, same gear box but huge difference in tyre size. Claimed speed on Bobby was higher than the milkman's favourite Rajdoot. Trying to dig up data sheets. The Bobby thread on forum is not having input for top speed.

Rajdoot GTS
Engine type: 2- stroke, reverse scavenged
Bore& stroke : 61.5 X 58 mm
Displacement : 173 cc
compression ratio : 1: 6.6
Carburettor : horizontal 24mm mikuni
ignition : Flywheel magneto
Power : 7.5 bhp @ 5000 rpm
Torque ( max) : 1.3 kg-m @ 3500 rpm
gear box: 3 speed constant mesh.
gear ratios : 2.89 , 1.47 & 1
Clutch : multiplate wet
Fuel tank capacity : 8 liters
oil capacity ( gear box) : 800 ml
generator : dynamo magneto 28 W
spark plug : mico HBW-175 Z.1
LENGTH : 167 cm
Width : 67mm
Wheel base : 112 cm
Ground clearance : 12 cm
Dry weight : 93 Kg.
Tyres : 3.50 X 10

[vikram_d]

Aren't Rajdoot GTS and "Bobby" the same bike?

"The Rajdoot GTS 175 was quite a popular bike during its time. Often refereed to as the monkey bike due to its hunched seating position and low powered engine, it was made more popular by Bollywood actor Rishi Kapoor when he used the motorcycle in the famous flick ‘Bobby’. It is from here that this bike got its Bobby nickname, which has stuck with its till now."

Source: https://www.cartoq.com/rajdoot-bobby...bike-restored/

[sudev]

Yes but for wheel size. And reported top speed was claimed higher.

[TN13Sleeper]

Originally Posted by sudev

To achieve top speed you need power to overcome this drag.

So extending the same logic of we change into smaller sized tyre would we achieve higher max speed?

Yes, Using a smaller circumference (outer diameter) tyre is a method of achieving the equivalent of a shorter final drive ratio. As a result of this, in the overdrive gear, you can touch much higher rpm.
But practically speaking, I predict the speed increase would be a marginal 5-10 kmph which doesn't matter for normal road usage.


By the way, did you try it out?

[sudev]

Been occupied with my dad's illness and care. Still on agenda.

5kmph top is good enough for the purpose I had in mind. Buddh Circuit holds pay and drive days.

[ishan12]

Simple Maths has the answer here.
Assumption-
Maximum RPM that can be attained at the wheel is the same.
Air drag is constant.
Torque delivered by the engine is the same in case of both tyres.
Both the tyres weigh the same.
In other words "All other variables remain constant except for the tyre circumference"

Speed = Distance covered per unit time

Scenario 1-
Tyre Circumference 1 meter
RPM at wheel - 10 rotation per second
Distance covered in one second =10 Meters = 10 m/s

Scenario 2-
Tyre circumference 2 meters
RPM at wheel - 10 rotation per second
Distance covered in one second =20 Meters = 20 m/s

So at a constant RPM, you will be at a higher speed with a bigger tyre.

Taking the example of a motorcycle, as the things are simpler to visualize.
In the above calculation, the RPM has remained constant, because the sprocket has not been changed, only the tyre has changed.
The only way to extract higher speed would be to change the sprocket to a smaller one, so that the wheel starts to spin at a higher RPM. However a smaller sprocket would mean lesser torque (Torque = Force x Perpendicular distance, distance has reduce due to smaller sprocket radius). So you attain the higher speed at the cost of reduced torque.

So to attain higher speed,
Use a bigger tyre on a smaller sprocket.
This is what my calculation says.

[condor]

Originally Posted by ishan12

Simple Maths has the answer here.
..
In other words "All other variables remain constant except for the tyre circumference"

Simple Math doesnt always work. If it did, esp in such cases, then manufacturers would have exploited it to the hilt.

The torque at the wheel is same in both cases of your example. A given amount of torque can only do a certain amount of work. In this case, it is distance traveled = rotation of the wheel. From your explanation, the same torque is doing twice the amount of work with the bigger wheel, and in the same time. Is that possible ?

[ishan12]

Originally Posted by condor

Simple Math doesnt always work. If it did, esp in such cases, then manufacturers would have exploited it to the hilt.

The torque at the wheel is same in both cases of your example. A given amount of torque can only do a certain amount of work. In this case, it is distance traveled = rotation of the wheel. From your explanation, the same torque is doing twice the amount of work with the bigger wheel, and in the same time. Is that possible ?

I just made it extremely simple for easier understanding as the thread title said "To go faster, can I use a smaller tyre?"
But theoretically it is the opposite. Rather you can just accelerate faster.

Lets get into a little more complexities.
In my last post I used sprocket size as an example to explain torque, and said "So you attain the higher speed at the cost of reduced torque."

We can use the same logic if we calculate torque at the point where the tyre meets the ground, and you will have below.

A wheel with bigger diameter will give you slower acceleration but higher top speed if the engine can develop enough torque.

A wheel with smaller dia will give faster acceleration but top speed will reduce.

However, to extract max power from the engine the vehicle needs to be in the meat of the torque curve, this may not be possible when you use very over sized/ under sized tyres, (Farther to the right from peak power with small tyres and to the left from peak power in case of large tyres )so theoretically you may attain higher speeds with bigger tyres, but your engine may not be able to take you to those speeds with limited power.
Which is why manufacturers set a final drive ratio/ gear ratio and tyre size to maximize performance.