# Calculating gear ratio for vertical climb

• Ortix
In summary, the problem involves using a human-powered bike-like machine to climb a 16 meter long rope. The total weight of the machine and human is 1300N and the theoretical force delivered by the human is 250 Newtons. A winch with a radius of 3.1 cm is used to climb the cable, and the goal is to calculate the radius of the gear that must be attached to the winch. The desired cycling speed is 100 rpm. Various ratio equations were used in attempts to solve the problem, but no successful solution was found.
Ortix

## Homework Statement

The problem is that using a human powered bike-like machine we have to climb up a 16 meter long rope. The total weight of the machine + human is 1300N and the theoretical force delivered by the human is 250 Newtons. The crank is 17cm long (that's the length of the arm, the radius of the gear is 11 cm). We are using a winch to climb up the cable. The winch has a radius of 3.1 cm. We now have to calculate the radius of the gear that has to be attached to the winch. The two gears will be connected with a bicycle chain.

After some research we came to the conclusion that we want to cycle at around 100 rpm.

## Homework Equations

There's a bunch of ratio equations we used. They are really simple and i doubt they are necessary to put on here.

## The Attempt at a Solution

The attempt is very very long. We took several approaches. We always end up with a smaller gear at the top (where the winch is) in contrast to the cranked gear. This kind of seems impossible to us since we are trying to get a light gear ratio where teh cyclist doesn't have to push too hard to lift the entire system.

So we assumed that the input force would be 250 Newtons and the output would be 1300. What we did think of is that the crank is able to deliver a moment but we were unsure on how to include that in our calculations.

Ultimately we ended up with nothing.

This is a very old image of our concept, but the general idea is the same. (the chain is not included)

Almost 400 views and no one is able/willing to help? I'm stuck on a dead end guys

## 1. How do I calculate the gear ratio for a vertical climb?

To calculate the gear ratio for a vertical climb, you will need to know the diameter of the gear and the number of teeth on each gear. The gear ratio is calculated by dividing the number of teeth on the driven gear by the number of teeth on the driving gear.

## 2. What is the formula for calculating gear ratio?

The formula for calculating gear ratio is: ratio = (number of teeth on driven gear) / (number of teeth on driving gear).

## 3. How does gear ratio affect a vertical climb?

Gear ratio affects a vertical climb by determining the speed and torque of the gears. A higher gear ratio will result in faster rotation, but with less torque, making it easier to climb vertically. Conversely, a lower gear ratio will result in slower rotation, but with more torque, making it more difficult to climb.

## 4. Can gear ratio be changed to improve vertical climbing performance?

Yes, gear ratio can be changed to improve vertical climbing performance. A higher gear ratio can make it easier to climb steeper inclines, while a lower gear ratio can provide more power for climbing over obstacles.

## 5. What other factors should be considered when determining the gear ratio for a vertical climb?

In addition to gear size and number of teeth, other factors to consider when determining the gear ratio for a vertical climb include the weight of the load being lifted, the slope of the incline, and the desired speed and power of the climb. It is also important to consider the strength and durability of the gears being used for the climb.

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