You have to measure the

mechanical advantage of the whole system. That's the ratio of the

crank length divided by the outside diameter of the rear tire times the gear ratio. That will give you the ratio of torque on the crank to torque on the rear wheel. Tire sizes are the approximate outside diameter, typically 26" for adults.

The force on the pedal varies with the angle of the crank. When the force is vertical and the crank is horizontal, you get the maximum torque from a constant force. The torque is then equal to the force times the crank length. Longer legs do better with longer cranks. A longer crank requires less force on the pedals. If the crank is too long, your bottom pedal may drag on the ground when you lean in a fast turn. (If you have

elliptical sprockets, they reduce the importance of the crank angle. They increase the mechanical advantage when the crank is close to vertical.)

You use a low gear uphill, and a high gear going downhill. If you have a gear box, count tire revolutions while turning the crank thru one revolution. To calculate the gear ratio of a derailleur system, count the teeth on the front and rear sprockets, F and R. The ratio is F/R. Your lowest gear uses the smallest front sprocket and largest rear sprocket. In this image, I count 40 teeth on the front sprocket and 28 on the rear sprocket. So the ratio is 40/28.

With 270 lb total on a 10% grade, you have 27 lb of tangent force on the tire. With a 26" tire, that's about 702 inch-pound of torque. With a gear ratio of 4:3, you need 702 * 4/3 = 936 inch-pound of torque on the crank. With a 6" crank, that's 156 lb

**average** force. You probably would not be able to get up that hill because your 200 lb weight can only be applied perpendicular to the crank shaft for a small part of the time. You would do much better with a 1:1 gear ratio and a 7" crank. An elliptical chain ring might also help on those steep hills.