[Sutripta]

Originally Posted by condor

Simple Math doesnt always work.

Simple maths works just fine, if one knows what one is doing. Wrong assumptions (like not realising initially at least, that max speed is power limited) leads to incorrect conclusions.

Regards
Sutripta

[Samurai]

I agree with Sutripta, simple math is enough to prove nothing changes. Although reduction in tyre weight will give some advantage.

Originally Posted by ishan12

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

This example is flawed, it completely ignores the torque formula.

T = F * r OR F = T/r
(I am ignoring sin θ since it remains the same)

Circumference = 2PI * r

If circumference has doubled, then radius has doubled. (2 & PI are constants)

Back to F = T/r, if torque is same and radius has doubled, the force applied on tarmac will be halved. There is no way the wheel will turn at same speed. It will turn at half the speed since only half the force is applied at tarmac. You will only cover 10 m/s like before, assuming both tyres weigh the same.

[srini1785]

+1 to both of the above posts. If engine rpm remains same, then changing to smaller tyres is not going to increase speed. Talking motorcycles, for higher speeds with same engine, you change to a sprocket set with higher teeth ratio rather than changing the tyres. This applies only up to a point.

[Samurai]

When people upgrade alloys and wheels, the only factor that impacts performance (speed at a given torque) is the new weight of the tyre+wheel combo. If you upgrade to a heavier combo, the speed will reduce. If you upgrade to a lighter combo, the speed will increase.

Size doesn't matter (thanks to F=T/r), weight does. Can't get any simpler than that...

[ishan12]

Originally Posted by Samurai

I agree with Sutripta, simple math is enough to prove nothing changes. Although reduction in tyre weight will give some advantage.

This example is flawed, it completely ignores the torque formula.

T = F * r OR F = T/r
(I am ignoring sin θ since it remains the same)

Circumference = 2PI * r

If circumference has doubled, then radius has doubled. (2 & PI are constants)

Back to F = T/r, if torque is same and radius has doubled, the force applied on tarmac will be halved. There is no way the wheel will turn at same speed. It will turn at half the speed since only half the force is applied at tarmac. You will only cover 10 m/s like before, assuming both tyres weigh the same.

Hi Samurai,

Yes your calculation is correct, however I think we are mixing speed and acceleration here.

My simple calculation pertains to achievable top speed at a given max RPM with different tyre sizes.

Since the thread is titled "To go faster, can I use a smaller tyre?", so by faster do we mean accelerate faster or higher top speed?
Because the answer in both the case differs.

Thus, in my next post I wrote below

Originally Posted by ishan12

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.
.

Please go through below article and video link to see this practically.

https://www.carthrottle.com/post/how...t-performance/

https://www.youtube.com/watch?v=wsaSslvEEiI

[Samurai]

Originally Posted by ishan12

Yes your calculation is correct, however I think we are mixing speed and acceleration here.

I was responding to whether speed can change with tyre size, when the torque and tyre weight remains same. We have established that speed at a given torque remains same.

Originally Posted by ishan12

My simple calculation pertains to achievable top speed at a given max RPM with different tyre sizes.

Top speed is a different matter because it depends on two independent parameters, top toque and top rpm of the engine. Power is nothing but torque * rpm. Only rpm has a direct relation (total gear ratio) with speed, torque doesn't.

Originally Posted by ishan12

Since the thread is titled "To go faster, can I use a smaller tyre?", so by faster do we mean accelerate faster or higher top speed?

I had discussed the difference in the English thread last month. When people say faster, they generally mean higher velocity. Acceleration is rate of change of velocity. So when you say accelerate faster, do you mean higher acceleration or jerk (rate of change of acceleration) ?

Looking at OP's question, I am thinking he simply means higher top speed. So, let's look at that.

If you put a bigger tyre and try to maintain the same top rpm, you will need proportionally more torque than before. If the engine can deliver that extra torque, your top speed will increase. If extra torque cannot be delivered, the rpm will drop proportionally, and the top speed will remain same (F=T/r). If you put a smaller tyre and maintain the same top rpm, you will use less torque and your top speed will decrease. This is the example shown in the video you shared.

If the top speed of a car is limited by top rpm and not top torque, you can increase top speed by using bigger tyre.

If the top speed of a car is limited by top torque and not top rpm, using bigger tyres will add only weight and actually reduce the top speed.

[Jaggu]

Originally Posted by sudev

Most of the modern cars have overdrive gear ratio in fourth and fifth gears. This is great for economy and general driving.
====
Expert's please advise before I spend money only to discover this theory is flawed.

It is also counter to what most people do by going in for tyre size upgrade.

Too complicated sirji! not an expert but... generally best to stick to stock tyres. i.e If you don't want to change too much on the acceleration, as well as the top speed parameters. The online wheel size calculators generally give a range of + or - 3% (if I am not mistaken) as a safe range within which you can play around, without adversely affecting these.

If you have a specific car in mind where you want to see how a tyre size change would affect, do post all the specs (engine output, gearing, final ratio, wheel spec old and new etc). With that some amount of confirmation can be done, if changing tyre size would help.

Personal experience I have had - Thar when I moved from 29" to 31" the acceleration decreased, but top end was similar since I was running a remap. Grand Vitara 2.4 auto - 225/60 to 235/65 did not make much of a difference, intact the acceleration was smoother and gear shifting more smooth, especially when aggressively accelerating.

[Sutripta]

Originally Posted by ishan12

so by faster do we mean accelerate faster or higher top speed?

Higher top speed.
In normal road cars top speed is normally power limited.
In agricultural tractors top speed is gearing + rpm limited. You don't want one of these barreling down the highway at 120 Km/ hr.


Regards
Sutripta

[raystriker]

You can go faster if you make things lighter. Technically, you can get skinnier, lighter tires and larger yet lighter forged wheels. (To keep the overall wheel diameter the same so that traction control doesn't freak out). This decreases the rotational mass and will increase handling, acceleration and even top speed. But it probably isn't available for you car or getting custom everything isn't worth the money.



This is the reason most high end performance cars are equipped with carbon fiber/ magnesium alloy wheels.

[venkyhere]

all we are interested in, is to find an optimal combination of gear ratio (including final drive) N , AND the overall wheel radius R, such that , when the engine is at its max BHP rpm, say "bhp-max-rpm" that is well before the revv limiter kicks in ,
the value v = (bhpmax-rpm)/N * R is the highest value.

Let's say that the car's engine has X bhp that it is capable of making. When the car is near its top speed,
bhp produced = func1 (rpm) = K1.v^3 + losses.
bhp produced = func1 (rpm) = K1. (rpm/N * R)^3 + losses ---> equation1
The func1 is the bhp v/s rpm plot, where bhp keeps increasing with rpm, peaks, and then falls off for further increase in rpm.
There is a sweet spot rpm, which we already called 'bhp-max-rpm' where equation1 reads :
func1(bhp-max rpm) = X

Now, N is already chosen by the carmaker, we can't touch it, so the only choice is R.

Make the R too big, and that will lead to situation where the func1(rpm) will dictate the game in equation1, and lead to a situation where the drop in rpm value will more than offset the increase in R, compared to the stock situation. The power produced will be a value less than X. Effectively 'v' will be a value less than the highest it can possibly be.

Make the R too small, and that will lead to a situation where the func1(rpm) value will be such that the rpm value will become high, go beyond the sweet rpm value 'bhp-max rpm' and reach a higher rpm where the power produced will be a value less than X. Lowering R has increased the rpm value beyond the sweet spot and still the rpm has not increased by the same factor as the decrease in R, inorder to result in a higher v. Effectively 'v' will be a value less than the highest it can possibly be.

So equation1 is a sort of push-pull between a cubical on the RHS with a non-linear curve on LHS. My guess is, that the people who make these cars, have already chosen a perfectly fine R, that equation1 will hit the sweet spot X bhp, landing nicely rpm=bhp-max-rpm, such that v is at highest value.

[raystriker]

Originally Posted by venkyhere

My guess is, that the people who make these cars, have already chosen a perfectly fine R, that equation1 will hit the sweet spot X bhp, landing nicely rpm=bhp-max-rpm, such that v is at highest value.

In an ideal world maybe, but for budget or non performance cars they probably look in the parts bin and choose whatever is available, cheap and will "work".
I didn't follow your math (I could, I just don't have the time) but do you factor in aerodynamics and other parasitic losses??

[venkyhere]

Originally Posted by raystriker

In an ideal world maybe, but for budget or non performance cars they probably look in the parts bin and choose whatever is available, cheap and will "work".
I didn't follow your math (I could, I just don't have the time) but do you factor in aerodynamics and other parasitic losses??

the cubical term on RHS is the power that goes into overcoming air resistance. The 'losses' are items downstream of the flywheel, things like drivetrain friction losses, tyre heat etc

[ishan12]

Originally Posted by Samurai

If the top speed of a car is limited by top rpm and not top torque, you can increase top speed by using bigger tyre.

If the top speed of a car is limited by top torque and not top rpm, using bigger tyres will add only weight and actually reduce the top speed.

Originally Posted by venkyhere

There is a sweet spot rpm, which we already called 'bhp-max-rpm' where equation1 reads :
func1(bhp-max rpm) = X

Originally Posted by ishan12

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.

I believe what we are all trying to say here is in essence the same.