# Hp vs weight; acceleration comparison

1. Oct 3, 2012

### newman180

I am working on an engineering project for college and have run into an unexpected wall.

I thought that my approach would work, but I'm not sure if I am getting reliable results and wanted to check on the proper method.

I am trying to calculate how long it would take a mass to accelerate to a given speed from an initial speed with a set input force.

So basically I'm comparing two different situations-

v1 = 15 m/s v2 = 32 m/s

1) 140 kg 25 hp
2) 150 kg 27 hp

I need to see the differences in acceleration (the time it takes to accelerate or distance it takes to accelerate) so that I can size components accordingly.

Total distance and other variables like air resistance or friction are not important right now.

Using the different newton laws, kinetics equations, etc. I can find a general % difference but since time, distance, acceleration are always directly correlated, when I change one value the power requirements stay the same.

This site http://www.engineeringtoolbox.com/car-acceleration-d_1309.html does something close to what I am looking for, but my calculations are the same as they display, but their output gives different results

This site http://www.baranidesign.com/acceleration/acceleration.html applies the situation almost exactly, but their math is not stripped down enough for me to apply it.

I must be missing something simple, yes?

Let me know if clarification is needed.
Thanks

2. Oct 3, 2012

### Simon Bridge

Welcome to PF;
You need to state how their output differs from yours in the first example and how you need the math "stripped down" in the second. Also - why it matters: what do you need these sites for anyway?

It will also be useful to know what level you are doing the project at.
Are you assuming constant acceleration? What is providing the accelerating force?

hp = horse-power? Why not use Watts?

3. Oct 3, 2012

### newman180

Hi Simon,

On the first website, my acceleration value and force values match, but the distance value is off by a magnitude of roughly three. When following their standard formula, my distance value is replicated. Why their's is different, I do not know.

The second website does not demonstrate all the formulas. Since there is no indication of calculating forces and distances, there is more "math" going on in the background that they have not documented. I would like to mimic their calculations so that I can fine tune it to my application.

The sites are merely for example of what I am trying to solve. Ultimately I am inputting formula's into a large spreadsheet to plot graphs for comparison.

It is assumed to be constant acceleration. The accelerating force is a small ICE, hence the use of HP. As most would know, to get to watts from hp, we just multiply by 746.

Thanks!

4. Oct 3, 2012

### Simon Bridge

The first website has a calculator where you input speeds in kmph and time in seconds ... if I test it out with initial speed = 0, final speed = 3.6kmph (=1m/s) I get 1m/s/s as expected.

If you didn't convert the units, you would be out by a factor of 3.6.
Since you have the same equations, you can write the program.

The second site provides all their equations at the top. They are taking into account quite a few more variables than the first one, like drag.

You don't want the second one then - they are using variable acceleration formulae. You should be fine with normal kinematics.
... so you know the input horse-power because it's written on the engine or something, OK, no worries.

5. Oct 3, 2012

### newman180

Thanks for the quick responses!

This is the output prompt and my excel sheet. You can see that the distance is the factor which is off.

Very true, but at the bottom of the calculations it gives me the information I'm looking for. Time it took to accelerate from 15-32 with 25 hp and 140 kg. As a bonus it told me how far a distance it traveled.
I would like to replicate this similar calculation if you wouldn't mind helping me, please.

Where is the distance in the calculation? Where does little "a" apply?

Yes, sorry, did not mean to come off the wrong way. I am working with a manufactured 25 hp engine. The general idea is increasing its output while minimizing weight.

6. Oct 5, 2012

### Simon Bridge

Since you won't get more that 25hp, this means minimizing losses, and maximizing time (if you want to maximize work). The motor will have a torque rating too I bet.

You want to know the distance travelled and time taken for a particular delta-vee at fixed power.

I don't think you can assume constant acceleration ... for fixed P and a, v=P/(ma)=constant; which would be a contradiction. You could insist on a constant acceleration restricted by maximum power available?

Going with the constant power throughout the motion:

Time taken: $T=P/\Delta K$

$$T=\frac{2P}{m( v_f^2-v_i^2 )}$$ ... displacement is the area under the v-t graph:$$d=\int_0^T v(t)dt$$ $$P=\frac{dE}{dt} = v\frac{dv}{dt} \Rightarrow v(t)=\sqrt{2Pt}$$... assumes adding energy at a constant rate.

That should get you started.