Calculating the power required to move a load up a gradiant

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In summary, the conversation discusses designing a system for a cart machine to carry a load up a hill with minimal assistance. The problem at hand is calculating the necessary power for the motor to move the load. The equation identified for this calculation is P=MxGxSIN(Angle)xV, with the variables constantly changing. The suggested power needed is around 169w, but due to motor inefficiencies, a half horsepower motor is recommended.
  • #1
Aquadust
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HI

Any help with this problem would be much appreciated.

I am designing a system in which a cart type machine needs to be able to carry a load up a hill with almost no help from the person pushing, My question is how do I calculate how much power is needed by the motor to move the load.

I know:
Total Load = 40KG
Maximum Incline = 14Degrees
The speed it will travel between is 1-4 MPH


I believe the relevant equations are P=MxGxSIN(Angle)xV
Also I am not sure but J=FxD

D=Distance
F=Force
J=Joules
M=Mass
G=Gravity
V=Velocity
P=Power

I believe its 40x9.81xSin14x1.78m/s = 169w

I just want to make sure this equation is right and if not what equation I need to use. it would be handy to have an equation as the variables are constantly changing.

Many thanks in advance for your help.
 
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  • #2
Looks OK to me, at 4 mph max speed. 169 w is about a quarter horsepower. Due to inefficiencies in the motor, I'd opt for a half a horse motor.
 

FAQ: Calculating the power required to move a load up a gradiant

How is power calculated for moving a load up a gradient?

To calculate the power required to move a load up a gradient, you need to know the mass of the load, the slope of the gradient, and the velocity at which the load is being moved. The formula for power is P = (mgh)/t, where m is the mass, g is the gravitational constant, h is the height of the gradient, and t is the time it takes to move the load.

What is the role of mass in calculating power for moving a load up a gradient?

Mass plays a crucial role in calculating power for moving a load up a gradient. The more massive the load, the more power is required to move it up the gradient. This is because the load's weight is directly proportional to its mass, and thus, a heavier load will require more power to overcome the force of gravity and move up the gradient.

How does the slope of the gradient affect the power required to move a load?

The slope of the gradient also plays a significant role in determining the power required to move a load. The steeper the gradient, the more power is needed to overcome the increased force of gravity. This is because the gravitational force is proportional to the slope of the gradient, and a steeper slope means a greater force is acting against the load.

Is the velocity of the load important in calculating power for moving up a gradient?

Yes, the velocity of the load is an essential factor in calculating power. The faster the load is moving up the gradient, the more power is required to maintain that velocity against the force of gravity. This means that a load moving at a higher velocity will require more power than a load moving at a slower velocity.

Can power be reduced when moving a load up a gradient?

Yes, power can be reduced when moving a load up a gradient by increasing the efficiency of the system. This can be done by reducing friction between the load and the gradient or using a more efficient method of power transfer, such as using gears or pulleys. Additionally, spreading the load over multiple trips or using a lighter load can also reduce the power required to move it up a gradient.

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