# Calculating Torque for a 21,000 lb Merry-Go-Round at 4 RPMs: A Design Challenge

In summary, you need to calculate the torque required by the inner ring gear to turn the merry-go-round at 4 RPM. You should also take into account losses and efficiency along the way.
Hi everyone,

I'm charged with designing a merry-go-round for a class project. It is to be driven by an electric motor and I chose to power it with a gear train. I need to pick a specific horsepower motor to drive the pinion and subsequent gears after it, finally leading to an inner ring gear that turns the whole structure.

My question is this, if the whole merry-go-round weighs about 21,000 pounds, how do I determine the amount of torque the inner ring gear must be applied to turn it at a speed of 4 RPMs?

I've got a good start but am not confident with my answer. I calculated the inertia of three separate bodies that comprise the merry-go-round and found that to be about 108,000 lbf-ft^2. At 4 RPM, I calculated the angular acceleration of the 36'-diameter merry-go-round to be 0.00833 rad/sec^2. I've found some equations online that say torque is equated by this equation:

τ = (I/g)*α and I got about 27.98 lbf-ft. That seems low for a 21,000 lb merry-go-round.

Can anyone on here tell me if I am correct or where I possibly went wrong?

And also could anyone give me any insight as to configure my gear train between the inner ring gear and the motor to accurately size the motor?

Thanks a lot!

First. In order to get a clearer picture of the system requirements, you must think of the process the other way around (i.e. not from motor to driven wheel). You must first start with the big wheel, then work your way backwards out to the motor, taking into consideration losses and efficiency along the way and then adding a factor of safety. If that's how you are already thinking of it, great!

Some math errors, not sure where you went wrong, but:
21,000 lb converts to 652 slugs.
I = .5 * 652 * 18^2 = 105652 slug-ft^2

T=I*a = 105652 slug-ft^2 *.00833 rad/s^2 = 881 lbf-ft

Try it in metric and you'll get the same thing!

## 1. How do you determine the appropriate size for a merry-go-round?

The size of a merry-go-round is typically determined by the available space and the intended age range of riders. It is important to consider factors such as safety, accessibility, and the number of riders that can comfortably fit on the ride. The average size of a merry-go-round is around 30 feet in diameter.

## 2. What materials are commonly used in the construction of a merry-go-round?

The most common materials used in the construction of a merry-go-round are wood, metal, and fiberglass. The base and support structure are typically made of wood, while the horses and other animals are usually made of metal or fiberglass. The use of these materials ensures durability and safety for riders.

## 3. How do you ensure the safety of riders on a merry-go-round?

Safety is a top priority in designing a merry-go-round. The ride should be constructed with high-quality materials and undergo regular maintenance and inspections. It should also have proper safety features such as safety bars and handrails. The ride should be designed to prevent entrapment or entanglement of riders and have a maximum weight limit for riders.

## 4. What is the average cost of designing and constructing a merry-go-round?

The cost of designing and constructing a merry-go-round can vary greatly depending on the size, materials used, and design elements. On average, a small, basic merry-go-round can cost around $10,000, while a larger, more elaborate one can cost upwards of$50,000. Additional costs may include permits, site preparation, and installation.

## 5. How do you choose the design elements for a merry-go-round?

The design elements for a merry-go-round can vary greatly and are often chosen based on the theme or location of the ride. Common design elements include different types of animals, colorful lights, and music. It is important to consider the target audience and create a design that will appeal to them. Collaborating with an experienced designer can also help in choosing the best design elements for a merry-go-round.

• Mechanical Engineering
Replies
1
Views
5K
• Mechanical Engineering
Replies
1
Views
2K
• Mechanical Engineering
Replies
8
Views
29K
• Mechanical Engineering
Replies
2
Views
6K
• Mechanical Engineering
Replies
11
Views
6K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• General Engineering
Replies
2
Views
3K
• Mechanical Engineering
Replies
6
Views
3K
• Introductory Physics Homework Help
Replies
3
Views
9K
• Mechanical Engineering
Replies
2
Views
4K