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Power Calculator

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Conditions

Simple Vehicle Power Calculator

 

What the Calculator Does.

 

The power needed to propel a vehicle can be determined by combining the force that needs to be applied to the vehicle to move it, with the vehicle speed at which this propelling force must be sustained. What the calculator does is help calculate the size of this drive force, you then tell it the speed at which you want the vehicle to move under the drive conditions being considered and it tells you the drive power.

 

Don't worry here if I'm not mentioning torque (isn't that what you need in drive wheels though?) - drive torque, through the traction generated by the vehicle's wheels, produces drive force at the tyre/road contact - it is this drive force that moves the vehicle. At the design stage it's easier to frame the calculation around this drive force rather than the drive torque.

 

A disclaimer might be in order first. The results produced are what can best be described as design estimates. The physics of this problem is generally well understood, but it is simplified here; perhaps more importantly though the data you provide about your vehicle (especially if it is at the design stage) is likely to be estimated and the accuracy of the calculation results will reflect both the accuracy of your input data and the simplifications of the method. Use the results as a guide only!

 

 

Inputs

The total drive force that has to act on the vehicle to make it move (or keep it moving) can be estimated by adding together individual force components that arise from different physical effects. These are: force to push up a gradient, force to overcome the rolling resistance of the wheels on the drive surface, force to overcome aerodynamic drag and force to accelerate the vehicle's mass. If you also want the vehicle to push or pull something then the force required to do this may also have to be added. There may be other effects but these are usually the main ones.

You can see straightaway that different driving circumstances will give rise to different sizes and combinations of these forces - eg for the purposes of the calculation is it on a hill or on the flat, is it running at steady speed or is it accelerating  etc etc? You need to decide what driving condition your calculation relates to,  are you trying to calculate maximum required power (to set maximum motor size for example), or power under average running conditions (to determine average energy usage and hence battery life for example), or power under specific known conditions (eg to answer a question like "what happens if I drive on grass instead of on tarmac?") or indeed for any other circumstance you might think of.

So, input no.1 is your brain power - the calculator does some of the math, it doesn't assess intelligently either your inputs or the results outputs - that's your job.

 

The other inputs are:            (Note for a version of the calculator with US (imperial) units click here.)

 

Basic Vehicle Data

 

Vehicle Weight     kgf

Vehicle Speed                  km/h

 

You decide if laden, partially laden or unladen weight is used - the more heavily loaded the vehicle is the bigger the power consumption. Speed is that at which vehicle power is to be calculated, note that the faster the vehicle goes the more power it needs. HINT - if you are towing another wheeled vehicle/trailer/implement adding its weight here will bring it into the calculation (underlying assumption is that the Rolling Resistance specified below applies to both vehicle and trailer).

 

Rolling Resistance

 

Coefficient of rolling resistance,     Cr   

 

Rolling resistance is dependent on ground conditions and tyre/wheel design. Click here for help and suggestions on what value to use. The calculator assumes a single Cr for the vehicle (ie all wheels/tracks have the same Cr). Normally the Cr figure relates only to the natural resistance of a wheel to roll - ie issues such as bearing friction are not included. If you are likely not to use low friction bearings you might increase Cr to compensate. Alternatively specify a drive transmission efficiency below.

 

Gradient Climbing

 

Angle of climb, 1 in                

 

Hill climbing can be a big contributor to required power - specify gradient in the form "1 in 10", "1 in 50", etc - anything flatter than 1:1000 will be taken by the calculator as on-the-level.

 

Aerodynamic Drag

 

Drag Coefficient, Cd     

 

Vehicle Frontal Projected Area,     m^2

or

Representative frontal width     m.    Representative frontal height     m.

 

Air Density    kg/m^3    

 

Drag is strongly speed dependent and is felt much more at higher speeds than low. If you have a slow moving vehicle this component of drive force might be well be ignored.

Drag coefficient is dependent on vehicle shape. Click here for help and suggestions.

Either input the frontal projected area directly or specify the width and height of the vehicle (the area will then be approximated at 0.9 x W x H).

A value is suggested for air density at normal atmospheric pressure.

 

Vehicle Acceleration

 

NOTE - This is an input to the power calculation, not an output. It allows the calculator to determine the power required to achieve the specified acceleration - you state the required acceleration.

 

Change in speed       km/h

Time taken to achieve this speed change      seconds

 

The calculator can work out the acceleration figure it needs if you tell it by how much vehicle speed changes over what period of time. For example 0 to 60 km/h in 10 seconds can be specified as a 60km/h speed change in 10 seconds, or a 6 km/h change in 1 second. 40 km/h to 60km/h in 2 seconds can be specified as a 20km/h change in 2 seconds. The calculator assumes that this magnitude of acceleration is present at the vehicle speed specified at the top of the page.

 

Any Additional External Force

 

Ext Force   kgf

 

This allows you to add in extra effects such as towing or pushing. If you have a tow bar pull you want to accommodate then you can add it in here.

 

Mechanical Transmission Efficiency

 

Effy  %

 

The calculated power is the ideal mechanical power required at the wheels to drive the vehicle under the conditions you describe. The motor output power will need to be more than this - because some is lost in the mechanical transmission. If you specify a transmission efficiency (in %) a figure for motor output power will also be calculated.

 

 

  

 

A new window will open with a summary of your input data and the calculation results. Use the browser's "Back" button return to this page to run a repeat calculation with different input data. This way you can build up a picture of how the results vary with design and/or operating condition changes.

 

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