The Wheels In the Sky

We need to start sizing things up. Because we will be dealing with one gear, similar to a fixed gear bike, we have to figure out a comfortable speed. There will be an average speed we will want to attain while traveling. It can't be too fast and dangerous and it can't be too slow either. The vehicle speed will be directly proportional to the speed the pump lever will be pumped. This also has it's limits concerning speed. People can only pump so fast. So how do we design for both? It all has to do with the gearing where the drive shaft meets the rear axle at the differential.

The rear axle with the differential has a gear ratio of 5 to 1. That means for every 5 turns the shaft of the differential makes, the wheels turn once. That's a pretty low gearing. If there were a direct connection from the pump lever to the shaft of the differential, that would mean for every 5 times the pump lever goes up and down the wheel would make one rotation. The diameter of the wheels we have are 26 inches, which is about 7 feet in circumference. What would a comfortable speed be in which to pump? Maybe 2 seconds for one up-down motion, or cycle. With a direct connection, pumping at 2 seconds per cycle we would get a speed of 0.465 mph. Too slow. We need to add gears, but how do we calculate our gear ratio?

This spreadsheet calculates the gear ratio. I haven't figured out how to make it interactive, but I can make it so individuals can collaborate on it...aka use it, if I get there email. Let me know if you want to play around with it. The following is how it works.

First choose how fast you want to pump and the desired speed you wish the cart to travel at. These fields are not highlighted. A series of calculations are performed and it outputs a gear ratio. Next you can choose the size of the gear for the drive shaft (labeled 2), or choose the size of the gear for the shaft of the differential (labeled 3).

As you can see the gear size can be related to inches. So this combination of a roughly a 20 inch diameter gear on the drive shaft and a 1.5 inch diameter gear on the differential shaft will give us the desired speeds.