The answers so far are exactly right as far as they go, but one might ask, why do bikes have such a much proportionally smaller contact patch than a car? It certainly is possible to ride a bike around with 30 psi of air in the tires, which would result in a similar contact patch to weight ratio. If you think about how a bike rides with nearly flat tires you are starting to understand the underlying reason.
Bikes have a relatively weak power supply compared to a car, which means that rolling resistance is proportionally much more important for a bike, and especially its rider. Rolling resistance, all other things being equal is reduced by hard high pressure tires. That is in part because the contact area is reduced, but also because less energy is lost to flexing the tire walls.
Cars on the other hand have relatively speaking lots of power and thus less concern for rolling resistance. That said you might wonder what would be wrong with very low rolling resistance tires? In a word, traction. It's much harder to design a high pressure low rolling resistance tire that will also have excellent cornering traction that cars require. It's much easier to achieve with a large contact patch, which as noted by others leads to lower inflation pressure. Commercial truck tires are designed for extremely low rolling resistance and therefore operate at higher pressure (between bikes and cars), but also suffer from relatively poor traction compared to cars. Low rolling resistance is very important to long haul truckers, high performance driving (cornering) is less important.
Its all a matter of performance tradeoffs. What's more important for the application? Low rolling resistance? Better traction? Lower cost? Bikes fall on the low rolling resistance therefore high pressure end of the performance spectrum and cars fall on the high cornering traction and therefore large contact patch low pressure end.
Interestingly there is a corollary question that could be asked that has the same basic answer. Why do bikes have larger diameter tires than cars? It turns out that all things being equal, the larger the diameter of the tire, the lower the rolling resistance. Bikes need low rolling resistance so they have big tires, same with commercial trucks by the way. Cars on the other hand have space and air resistance issues that drive the tire size down to a smaller optimal diameter.
Similarly tire width is also dictated by a balance between the demands of low rolling resistance and better traction.
Tread patterns are also subject to tradeoffs between low rolling resistance (no tread or straight grooves) and good traction especially in wet or muddy conditions (more aggressive tread and lateral grooves).
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I think you already knew this by, overdoing it a bit. but you take the cake.
You hold a persuasive argument my friend.
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Because they have much less contacting surface area to support the weight of the rider. Since Pressure = Force / Area, if area gets smaller, pressure gets higher.
So what about those Really thin tires, that have the thin strip along them?
Both frollard and steveastrouk have it. Good show gents!
It's a function of area, a square function :)
say a bike is 200 pounds with rider. That bicycle has probably around 3-5 square inches of rubber on the road...that means it exerts about 40-65 psi on the road
A 2000 pound car has 4 tires on the road...500/tire - with anywhere from 10-20 square inches each...25-50 psi at the road.
dragsters with gigantic tires run at very low pressure not only because they need the ballooning effect for speed, but because its all about pressure at the road.