I am doing a project on controlling wheels of a wheelchair. The diameter of the wheel is about 25-30 inches, the weight which the wheelchair is supposed to carry is upto 80 Kgs and it should run at a speed of 0.5-0.7 metres per second. I thought of using a 24V dc motor, what speed and Power must the dc motor provide to move a wheelchair at above specifications.
What speed and Power must the dc motor provide to move a wheelchair at above specifications.
Wheel RPM = chair_speed / Wheel-diameter x 60
Motor speed = wheel speed/Gear_ratio.
Motor power = hard_without_more_data.
Factors include: Friction, gear train efficiency, motor efficincy, carpet-lino-concrete- ..., slope or flat, ...
Look at existing chairs.
2 x 500 Watts seems good in many cases. Lower or even much lower may be OK in your case.
In a demonstration version on a smooth hard floor with a good motor and gearbox and smooth hard wheels I'd expect that 100 Watts would probably be acceptable.
At your target speed losses from windage are minimal.
Adjust (increase) any of the following for losses due to motor efficiency (say perhaps 80-90%) and gearbox efficiency (90-95%?)
Power due to air resistance can be determined from the drag equation.
Drag = 0.5 x Air density x Area x Coefficient-of-drag x velocity-squared
Power = Drag x velocity.
Power (Watts) = 0.5 x 1.2 kg/m^3 x A x 1 x V^3.
A in m^2
V in m/s
Cd = 1 = flat plate drag - about right for a wheelchair
At 1 m/s and 1 square metre area Power = 0.6 x 1 x 1 x 1^3 = 0.6 Watt!
At 2 m/s (7 kph) Power 5 Watts.
At 5 m/s (18 kph) Power = 75 Watts
ie in a "still air" environment or where minor air movement occurs power loss to windage is liable to be under 10 Watts. In external gusty wind" environments substantial power peaks may occur.
If the wheelchair travels on an ascending (non level) surface then extra power will be required to provide the potential energy thus achieved by the gain in height.
Energy required to move m kg upwards against gravity g a height h
E = mhg
g id about 9.8 m/s/s which can be approximated to g = 10 for this sort of working. In SI units m kg, h m, v m/s, g m/s/s:
Energy = 10.m.h Watt,seconds.
To achieve this in time t seconds
Power = E/t = 10.m.h/t.
Power required = 10.m x the height increase per second.
For a wheelchair travelling a V m/s up an incline of d degrees,
Height increase per second = v.tan(d)
Power due to slope = 10.m.V x tan(d)
For eg a 5 degree slope at 1 m/s and a 100 kg all up load
Watts = 10.m.v.tan(d) = 10.100.1.tan(5) ~= 90 Watts
ie power required to ascend a slope is non trivial above a few degrees.
For a 1 in X slope
x = 1/(tan(d))
So a 5 degree slope = 1 in 1/(tan(5)) = 1 in 11.4