Tiny cars can fare well in standard crash tests that pit a vehicle against a wall. But they look vulnerable on the road for a reason–a study released today by the Insurance Institute of Highway Safety shows they’re no match for bigger cars.

The report’s release coincides with the the New York Auto Show, where the automaker Smart, which is based in Stuttgart, Germany, has a special display designed to assure American customers that its cars, including the Smart Fortwo, are safe. A cutaway version of the Fortwo shows its protective cage and air bags, and signs proclaimed its good crash test ratings.

But the report released today says that for all these protective measures, the laws of physics still put smaller cars at a disadvantage. As the report explains, the forces that act on occupants depend on two factors–weight and size:

When a car crashes into a solid barrier, the outcome depends in part on the size of the front end. If one car’s front end is long enough to crush twice as much as another car’s in a barrier crash at the same speed, its restrained occupants will experience half as much force as the people in the smaller car because it takes them twice as long to stop.

When two cars going the same speed crash front to front, the outcome depends in part on the cars’ relative weights. The heavier car will push the lighter car backward during the impact, which means the velocity change of the heavier car will be much less than that of the lighter car. If the lighter car weighs half as much as the heavier car, the forces on its occupants will be twice as great.

For example when two cars collide with each going 40 miles per hour, and one of them weighs twice as much as another, “the heavy car pushes the light one backward at 13 miles per hour. The velocity change of the light car (53 mph) is twice that of the heavier car (27 mph).”

In the tests, the Insurance Institute drove minicars into mid-sized cars, with each travelling at 40 miles per hour. It crashed a Honda Fit into a Honda Accord, a Smart Fortwo into a Mercedes C class, and a Toyota Yaris into a Toyota Camry. You can see the results of the impacts in the video here. The small cars fared much worse in terms of the destruction of the passenger area and forces detected on dummies. The results are echoed by real-life statistics: “The death rate per million 1-3-year-old minis in single vehicle crashes during 2007 was 35 compared with 11 per million for very large cars.”

Of course, small and light cars have a lot going for them. In addition to using less gas than big ones, they can reduce congestion in cities, which is itself a great way to reduce gas consumption because it decreases the amount of time spent idling in traffic. Making cars smaller and lighter is also a cheaper way to save gas than converting cars into hybrids–cheaper approaches can spread through the vehicle fleet faster than expensive ones, so their total impact on gas consumption would be greater.

Is there a way to promote smaller vehicles without sacrificing safety? Congestion regulations, like those in London, could keep large vehicles out of certain parts of cities, with exceptions for delivery trucks, emergency vehicles and mass transit. Today many cities safely accommodate both pedestrians and large vehicles with the help of sidewalks and curbs. Special lanes could keep small vehicles safe. Maybe the safest way to reduce gas consumption is to get people out of cars altogether and into trains and buses. Or maybe CAFE regulations can be structured to ensure that all cars and light trucks get lighter–after all, it’s the relative size that counts. Of course, today’s larger vehicles will still be on the road for a decade or more, even with such changes.