# Faster Small Tires vs Slower Large Tires [closed]

We have two tires with radius r and R respectively. They are connected to two almost identical vehicles with same net mass.

"Almost", because Gear ratios are adjusted such that At equal Engine RPMs, both vehicles have same road speed, on paper at least.

So, does this have any effect on the offroad performance, hauling performance, fuel efficiency, and power output of the vehicle? What else effect could wheel size have?
Would the effect be different for different vehicle builds, like semi-trucks, minivans, bikes, muscle cars, and race cars?

This question is just a thought experiment, so contruction cost, logistics, looks of vehicle etc do not need to be considered.
r is small radius and R is large radius

• Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
– Community Bot
Jun 29 at 6:36
• Vehicles perform differently between two same-sized but different design tires. Very complex issues involved. Jun 29 at 11:14
• Not directly related to your question, but roads are not perfectly smooth, and when a wheel hits a bump in the road, it has to climb over. It's harder for a smaller wheel to climb over any given bump than for a bigger wheel to climb over it. If you hit a certain pothole at a certain speed on your bicycle, it might jolt you into a higher level of awareness of your situation. Hit the same pothole at the same speed on a stand-up scooter with itty-bitty wheels, and you might experience an unpleasant facial-pavement interaction. Jun 29 at 13:51

As per rolling resistance law, ratio of engine work done opposing rolling resistance force negative work ,in case big and small tires is : $$\frac {W_{_R}}{W_r} = \sqrt {\frac {r}{R}} ~~~~~~~~~~~~~~~~(1)$$, assuming same sinkage depth in both cases. $$W_{_R}, W_r$$ - rolling resistance negative work done of big and small tires respectively.

If sinkage depth $$z$$ depends on tire size (which should be, because bigger tires should have higher contact area with the ground, this in turn should reduce car pressure to the ground, and consequently - sinkage depth), then per coefficient of rolling resistance,

$$C_{rr}={\sqrt {\frac {z(d)}{d}}}$$

where $$d$$ is wheel diameter, relationship of work done ratio against rolling resistance force given in (1) can be more complex. In any case, as per (1) it is expected that a car with bigger tires will be more inertial, and thus will consume less fuel for keeping same speed. Conclusion, bigger tires will make car more fuel effective.

• So, Larger = Better? Jun 29 at 8:26
• There is no universal answer, there may be other factors as well. For example, in winter when static friction decreases due to icy road,- bigger sinkage depth could be advantage, because it would give better stability on the road. Thus in winter is probably more useful to have smaller and thinner tires. However, classical example illustrating usefulness of huge tires is to see monster truck riding over other cars,- you can't do that with "ordinary" car exactly due to rolling resistance threshold of classic car tires. Jun 29 at 9:11

Long distance trucks use large tires in part because of rolling resistance, as @AgniusVasiliauskas pointed out.

But also a large tire has a more gentle curvature. This means a larger contact patch. This means more traction for a race car. An off road car won't sink as deeply in sand or mud because of reduced pressure under the tire. This also means reduced tread wear.

When encountering a bump, large and small tires are deflected upward the same distance. But the large tire feels the bump sooner. The deflection takes place over a longer time interval and is gentler.

• So only reason our wheel aren't so big is awkward appearance and cost? Jun 29 at 12:12