# Tag: math

The Problem: I have two massive blind rollers that are operated by hand. I would like to explore the possibility to lift them using a combination of electric motors and gears.

The main idea is to figure out how to achieve that with very small motors, and have a system that would work not too slowly to be completely useless.

Following the information provided in this post, the problem can be decomposed into two:

1. The torque of the model. With the right gearboxes also a small motor could lift (slowly) a heavy weight, so that is something that needs to be explored
2. The rate of which the motor can lift the weight.

While the first one is difficult to calculate, the main idea for the second can be calculated using the following formula:

$W= m g h \over t$

Where W is the power required to lift a mass m of an height h in a time t.
It’s also possible to rewrite as the velocity v on which such mass gets lifted (because v = h/t):

$W = mgv$

So if we use 10Kg as weight, to lift this at a speed of 1 m/s would require a power:

$W = 10 \times 9.81 \times 1 = 98.1W$

This is just the beginning of the rabbit hole. I may post updates in the future if I will continue this. We will see.

How an Hill equation looks like?
What is the behaviour of an alpha function?

well, I have scipy installed, I know the equation, I know how to create an array of points… Let’s crunch some numbers!

Hill’s equation:

n variation

K variation:

Alpha function:

If you interested in this and other amenities check the code in the scipy_ex folder on github.

The Hill equation is in the mathematical functions script..

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