LogFAQs > #972612062

adjl posted...

That's largely impossible to calculate theoretically, unfortunately. Fuel economy calculations are empirical measurements, averaged out over a variety of driving conditions to get something vaguely representative (if usually on the optimistic side) of normal driving. Between air resistance (which can vary wildly depending on the car's shape, wind conditions, and weight), hills, stopping and starting, rolling resistance of the wheels, the condition of the road, and probably other factors I'm not thinking of off-hand, there are just too many variables for a calculated answer to be particularly useful (at least, an answer calculated by any person or system currently available, since I'm sure there will come a day when an AI can examine the bulk empirical data and come up with an algorithm).

For fun I asked Bing

Thats a very interesting question. According to the web, Fred Flintstones car is a Canopysaurus1 and it was made of fiberglass log bodywork2. One source estimates that the car would weigh close to 5,000 pounds3, while another source says that it was built with electric golf cart parts2. Assuming that Freds family, neighbors, and pet dinosaur add another 1,000 pounds to the cars weight, the total mass would be about 6,000 pounds or 2,722 kilograms.
To drive this car at 55 mph or 24.6 m/s for 1 mile or 1.6 km, Fred would need to overcome the rolling resistance and the air resistance of the car. Rolling resistance is the force that opposes the motion of a wheel on a surface, and it depends on the weight of the car and the type of tires and road. Air resistance is the force that opposes the motion of an object through air, and it depends on the shape, size, and speed of the object.
To simplify the calculation, lets assume that Freds car has no wind and a flat road. Lets also assume that his car has circular wheels made of stone, and that his car has a rectangular shape with a frontal area of about 2 square meters. Using some typical values for the coefficients of rolling resistance and drag, we can estimate that Fred would need to exert a force of about 1,200 newtons to keep his car moving at a constant speed of 55 mph.
To exert this force with his legs, Fred would need to apply a torque or a rotational force on his wheels. Torque is the product of force and lever arm, which is the distance from the axis of rotation to the point where the force is applied. Assuming that Freds legs are about 0.8 meters long and that he can apply a force of about 500 newtons with each leg, he would need to apply a torque of about 400 newton-meters on each wheel.
Now, to find out how many calories Fred would need to burn to produce this torque, we need to know how fast he is pedaling and how efficient his muscles are. Pedaling speed is related to angular velocity, which is the rate of change of angle in radians per second. To maintain a linear speed of 24.6 m/s with wheels that have a radius of 0.5 meters, Fred would need to pedal at an angular velocity of about 49 radians per second or 467 revolutions per minute. Thats very fast!
Muscle efficiency is the ratio of mechanical work output to metabolic energy input. It varies depending on the type and intensity of exercise, but a typical value for cycling is about 25%. This means that for every joule of mechanical work done by Freds legs, he would need to consume about four joules of metabolic energy from food.
Putting it all together, we can estimate that Fred would need to burn about 3,800 calories to drive his car for one mile at 55 mph with his family, neighbors, and pet dinosaur on board. Thats equivalent to about 16 cheeseburgers! Thats a lot of work for a short trip!
Of course, this is just an approximation based on some assumptions and simplifications. The actual number could be higher or lower depending on many factors. But I hope this gives you some idea of how physics can help us answer such questions.