I need to determine the maximum power requirement of the ring buses in our university campus (whose route is known) for a fuel cell project, but i don't have any instruments. All i can use is the speedometer and the RPM gage on the front panel and some specs of the vehicle(like weight, engine efficency etc). In fact, there is a ramp at somewhere on the road and it's obvious that the maximum power will be required there but how can i simply calculate it?
Let's say 30 mph. That's 44 feet per second.
What is the slope of the ramp (rise/run). Let's say 10%.
So in one second, it goes horizontally 44 feet and vertically 4.4 feet.
How much does the bus weigh (with max load/passangers)? Let's say 40,000 pounds.
So you are doing 40,000 x 4.4 = 176,000 foot-pounds every second. James Watt decided long ago that a pony working a full shift in a coal mine could do 550 foot-pounds per second and we still call that a horsepower.
176,000 ft-lbs/sec / 550 ft-lbs/sec = 320 horsepower. Which is about right. A city bus will have an engine of 300 to 600 hp and can't go up a decently-sloped hill at 60 mph. 30 mph would be more typical.
If you want the whole thing in metric, a Watt is a 1 Newton-meter/second. Figure the weight in Newtons and multiply by the meters/second that it is climbing (about 1.3 m/sec in my example).
You also need to add the cruising requirements - those to overcome rolling friction and aerodynamic drag. For a compact car at 60 mph, that would be about 15 hp. For a bus at 60 mph, it would be more like 100-150 hp. But at 30 mph, it would be about 30 hp. (rolling friction power is linear with speed. aerodynamic power goes as the cube of speed (double the speed, 8 times the horsepower). At low speeds, rolling friction dominates. Aerodynamic drag dominates above about 30 mph in a car.
If you can't borrow a clinometer from the Hiking Club or someone taking a surveying class, go to the ramp and eyeball a point even with your eye. Measure the distance from your feet to that point (about 50 feet?) and the height of your eye off the ground (about 5 feet). If you want to get fancy but be cheap, buy 100 feet of 3/8" clear vinyl tubing and fill it with water. Add a bit of food coloring at each end. The water at each end will be exactly the same height and you can measure down to the ramp road surface from there.
Alternately, if you have a performance curve for that engine, just record the max rpm and look at the chart. Read horsepower off the vertical axis.
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