# Relation between Power, Weight & Speed

Motor
I am going to use these 100rpm 12Volt Motor supplied Power given below.

Surface
Surface will be Plain Wooden. Area of contact between 6 Tyre and surface would be maximum of 4cm2 in total.

Use
They are basically Tyre for my Battle Bot

Direction
All 6 Motors will work in same direction to move my Bot Forward. Not climbing nor Coming down.

Tyre
I'm going to use these Tyre but with different diameter for each Motor (Information given Below).

Structure & Design
Here's a Scaled 3D Sketch of my Battle bot. In case you need it.

Voltage & Tyre Diameter

• 4 Motors with 7cm Diameter and Power Ratio is 5 (each).
• 2 Motors with 5cm Diameter and Power Ratio is 7 (each).

What I want is the Relation Between Supplied Voltage, Supplied Current, Weight of Bot and the Speed at which Bot can move.

I'm new to all this so Please tell me if you need more information about anything or if I have gone Wrong Somewhere.

• @jsotola there must be a mathematical equation to equate it all – 10011101111 Jan 14 '18 at 5:49
• @jsotola What else do you want? – 10011101111 Jan 14 '18 at 5:51
• An exact prediction cannot be made because the losses (friction is one) are unknown. Add the equations or relations that you know to your question and someone will help improve then. – hauptmech Jan 14 '18 at 7:12
• @hauptmech Well... now i have given area contact... you can atleast estimate friction now – 10011101111 Jan 14 '18 at 7:26
• Consider adding a picture or web-viewable 3d model. – hauptmech Jan 14 '18 at 7:44

The calculations are difficult. Here are some foundation equations. If you demonstrate interest and refine your question based on what you learn I'm sure that myself or someone else will help you build the equations to the detail you want.

The power equations are the easiest way to start.

## Input power

$P_{in} = EI$ where $E$ is voltage and $I$ is current.

## Output power

The output power is the motion of your robot.

$P_{out} = \nu f$ where $\nu$ is velocity and $f$ is force.

## Entropy

Power is the transfer of energy from one place (batteries in your case) to another (wheels). Every time we move energy from one place to another, some gets lost. We call these losses. Every equation for power (energy transfer) inside a system includes losses.

## Conservation of energy

The law of conservation of energy says that the amount of energy in a system does not change. Figuring out the actual boundaries of your system and writing appropriate equations can be challenging. However for your system as you have described so far, we can say that

$P_{out} = P_{in}$

Add in the fact of entropy and the equation looks like:

$P_{out} = P_{in} - (losses)$

# Basic relationship

By substitution, the basic relationship between input voltage, input current and speed is the following.

$EI - (losses) = \nu f$

Note:

1. Energy is transferred many times (from battery to wires to motor electronics to electromagnetic motor to wheel axle to wheel to ground) so there are many different losses that need to be estimated for accurate results.
2. Newtons second law says that a body in motion (your robot) will stay in motion unless acted upon from an outside force. So you need zero force to go your max velocity.

This means that you need zero power, plus lost power, to go your max velocity.

# Next steps

Energy is conserved. The power flows from the battery to the environment through the wheels. So the power is the same at every stage, minus entropy.

$P_{in} = P_{Hbridge} = P_{motor} = P_{wheels} = P_{robot}$ with losses at each stage.

The next step is to start writing more detailed equations for each of these stages so that we can estimate the losses.

You will notice that $f$ is unknown in the simple relationship above. So that is where you need to improve your question.

$f=m a$ where $m$ is mass and $a$ is acceleration.

Mass is constant for your current question, so you need to define what acceleration you need.

Usually we define a motion profile, which defines all the velocity and acceleration changes for all the tasks of the robot. In your case, we can simplify it. You probably just want the robot to accelerate up to maximum speed as fast as it can.

Given your motor specifications and wheel sizes, can you write an equation that estimates the acceleration of your robot if you have no losses? Add this to your question.