Calculating km/hr from engine rpm

[sozener1]

Homework Statement

the gear ratio between crankshaft and driveshaft calculates to be 13.579 at first gear

the diameter of the car wheel is 0.6m

the transmission efficiency is 0.85

weight of the car is 1200kg

if the engineer is running at 1500rpm how do you calculate the speed in km/hr generated by the engine

Homework Equations

The Attempt at a Solution

since gear ratio is 13.579 I multiplied it to 1500 rpm then by 60 to get revolutions per hour
and I multiplied result by (0.6*pi) to obtain the distance it traveled in an hour.

then I get something like 2000km/hr which I think is ridiculously high?

so I tried to divide 1500rpm by the gear ratio and then calculated, then I get somting like 12km/hr which I think is too low.

what have I done wrong

 

[Mark44]

Homework Statement

the gear ratio between crankshaft and driveshaft calculates to be 13.579 at first gear

the diameter of the car wheel is 0.6m

the transmission efficiency is 0.85

weight of the car is 1200kg

if the engineer is running at 1500rpm how do you calculate the speed in km/hr generated by the engine

Homework Equations

The Attempt at a Solution

since gear ratio is 13.579 I multiplied it to 1500 rpm then by 60 to get revolutions per hour
and I multiplied result by (0.6*pi) to obtain the distance it traveled in an hour.

then I get something like 2000km/hr which I think is ridiculously high?

so I tried to divide 1500rpm by the gear ratio and then calculated, then I get somting like 12km/hr which I think is too low.

what have I done wrong

You need to divide the engine RPM by 13.579 to get the wheel RPM. For every 13.579 revolutions of the crankshaft, the wheel goes around once.

So by very rough calculations, at 1500 RPM the wheels are turning at about 100 RPM. Each revolution of the wheel is ~ 2m, so the wheels are covering about 200 m/min. That works out to 12,000 m/hr or about 12 Km/hr, which is the same as what you got.

I think this is a reasonable result. The transmission in this vehicle is geared extremely low. With gearing this low, you could probably pull stumps out. The gearing for cars is typically in the range of about 3.0:1 to 4.5:1. Also, at 1500 RPM, the engine isn't turning very fast, with idle being somewhere around, say 800 RPM. A lot of cars have a redline above 6500, and some motorcycles have redlines up around 12,000 - 14,000 RPM.

Some of the data you posted is extraneous -- the weight of the car doesn't enter into these calculations, although it does play a role in the acceleration. Also, the transmission efficiency doesn't play a role, although it does affect the power at the rear wheels.

 

[sozener1]

You need to divide the engine RPM by 13.579 to get the wheel RPM. For every 13.579 revolutions of the crankshaft, the wheel goes around once.

So by very rough calculations, at 1500 RPM the wheels are turning at about 100 RPM. Each revolution of the wheel is ~ 2m, so the wheels are covering about 200 m/min. That works out to 12,000 m/hr or about 12 Km/hr, which is the same as what you got.

I think this is a reasonable result. The transmission in this vehicle is geared extremely low. With gearing this low, you could probably pull stumps out. The gearing for cars is typically in the range of about 3.0:1 to 4.5:1. Also, at 1500 RPM, the engine isn't turning very fast, with idle being somewhere around, say 800 RPM. A lot of cars have a redline above 6500, and some motorcycles have redlines up around 12,000 - 14,000 RPM.

Some of the data you posted is extraneous -- the weight of the car doesn't enter into these calculations, although it does play a role in the acceleration. Also, the transmission efficiency doesn't play a role, although it does affect the power at the rear wheels.

thank you so much for the detailed explanations it really helped

 

[Mark44]

Sure, you're welcome!

 

[DeeNos]

I would first like to clarify the units being used in this problem. Engine rpm is a measure of revolutions per minute, while km/hr is a measure of kilometers per hour. In order to accurately calculate the speed in km/hr generated by the engine, we need to convert the units accordingly.

To do this, we can use the following equations:

Speed (km/hr) = (rpm * gear ratio * wheel circumference * 60) / 1000

Wheel circumference = 2 * pi * (wheel diameter / 2)

Using these equations, we can calculate the speed generated by the engine at 1500 rpm:

Wheel circumference = 2 * pi * (0.6 / 2) = 1.89 m

Speed (km/hr) = (1500 * 13.579 * 1.89 * 60) / 1000 = 116.45 km/hr

This value seems more reasonable for a car's speed. It is important to note that this is the theoretical maximum speed that can be generated by the engine at 1500 rpm. In reality, other factors such as air resistance, friction, and road conditions will affect the actual speed of the car.