Quite the conundrum.. (1 Viewer)

[sneaky pete]

Bob recently attained a patent for a new electric skateboard design. Bob is curious as to what kind of motor he should purchase to accompany his new skateboard.
The maximum load Bob expects the skateboard to be able to carry is ~75kg. Bob hopes to travel at a speed of 12km/h (3.3m/s) up his favourite hill. The hill Bob likes to rid up has an incline of ~7° from the horizontal. Bob has a 12Volt dc SLA battery (7.2Ah) - 5hr rate (1.19A), The coefficient of friction (µ) between the wheels and the sidewalk is 0.4. Assume the acceleration due to gravity to be g = 9.8ms². Assume 5% energy lost due to friction in the gears. An world-wide-web address to a local, reputable motor dealer is provided below. Include any assumptions you make.

• What kind of motor should Bob purchase for his skateboard? (brusher direct drive, stepper, PM brushless, etc) taking into account the size of his skateboard (210mm x 805mm), ease of mounting, etc. Answer with reference to at least one principle you have studied this year. (3 marks)
  
• What kind of motor (in terms of RPM, Torque, etc) should Bob purchase? Use the information in the question, as well as any formulas you wish. Derivation of formulas is not necessary. (6 marks).
  
• Will Bob be able to manage to travel at his desired speed, using his trusty 12V (7.2Ah) battery? Why/Why not? Justify your answer mathematically. (4 marks).
  
• If Bob can reach his desired speed with his battery, which motor from the local dealer (Jaycar Electronics, WWW address provided below) should Bob purchase? Respond with either Stock-Code or catalogue number. Cost is not an issue.
  If you have determined Bob cannot reach his desired speed with his current 12V battery (7.2Ah), assume Bob's battery is now a 12V dc 18Ah (5hr rate - 3.05A). Include which battery you have assumed Bob will be using, in your response. (5 marks)

http://www1.jaycar.com.au/

 

[Xayma]

Hmm sounds more like an Engineering Studies problem, so you might try posting in there as well. Ill have a look later cause I dont feel like doing a friction problem on an angled plane at them moment.

 

[Xayma]

Im doing Number 3 Ill do the rest as I go

From a quick sketch it can be shown that the force acting down the plane is: gravitys component that is parallel to the plane and the friction, with the force pushing up is the motor.

Let the force of the motor be Q.
Since it is at equilibrium:
F_F+gravity acting down plane=Q
Q=μN+735sin 7°
=0.4*735cos 7°+735sin 7°
=381.383N

Now the power required (P_r)=Fv (derived from work formula)
P_r=381.383*3.3
=1 258.564Watt

He has no chance in hell of making it up. Of course the coefficient of friction wouldnt be that big, especially for kinetic friction.

 

[sneaky pete]

1.25kW?
a 200kg+ solar car can go about 85km/hr on a flat surface with the same power.. =(

Q=μN+735sin 7°
=0.4*735cos 7°+735sin 7°

where did that 735 come from?

 

[Xayma]

1.25kW?
a 200kg+ solar car can go about 85km/hr on a flat surface with the same power.. =(

Q=μN+735sin 7°
=0.4*735cos 7°+735sin 7°

where did that 735 come from?

75kg*9.8ms^-2=735N, you have to work in SI units.

That frictional force is extremley large, that skateboard wouldnt slide down a hill with a 20° incline.

 

[sneaky pete]

ahh i see, thanks.
what is a more reasonable frictional force to use?

 

[Xayma]

I dont know, but μ is given by tan α=μ where α is the angle at which it will start to move down a slope due to gravity (ie at the angle frictional force = the component of gravity that is parallel to the slope)

 

[lucky]

answering this question is gonna be painful...