I to figure out how to turn acceleration data into Horsepower/Torque

[soundengineer]

I have a vehicle with some known info...
weight: 3400lbs
Speed at a specific time: see data in chart linked below
overall gear ratio: 2.922
Tire size: 25.68 inch Radius
RPM at speed: see data in chart linked below

heres the data
http://spreadsheets.google.com/ccc?key=pxiQyAOYb5vb6jOOMdoQuOg"

where do I start??
I don't mind doing math...but I need some help understanding what I need to do and where I need to start.

I probably want to do this over a 1 second sample so that I don't have to do any x1000 or /1000 math in there...
I can convert the speed into Kph and the mass I can do in kg if it makes it easier

I hope to come up with a basic understanding of the math involved and do a little chart of Horsepower and torque vs RPM in the end

 

[buffordboy23]

I tried to a car analysis at one time. Here is a link with a lot of formulas:

http://www.rdrop.com/~/larry/download/formulas.pdf

See if this helps. I couldn't see your car data.

 

[soundengineer]

I tried to a car analysis at one time. Here is a link with a lot of formulas:

http://www.rdrop.com/~/larry/download/formulas.pdf

See if this helps. I couldn't see your car data.

not really...I can find all of those formulas and I understand them on their own...
its making them work together to get my formula here...

I know the mass and I know that it accelerates a certain amount over a given time...
how do I calculate horsepower for that given time...
I can set it at 1 second or 10 seconds...I don't care about teh interval...al I want to know is how to get from acceleration of 12mph in one second to horsepower value for that tme

 

[buffordboy23]

Did you try looking for any dyno chart data for your stock vehicle online? This could simplify your task tremendously.

I'll take a better look at your question when time permits.

 

[berkeman]

not really...I can find all of those formulas and I understand them on their own...
its making them work together to get my formula here...

I know the mass and I know that it accelerates a certain amount over a given time...
how do I calculate horsepower for that given time...
I can set it at 1 second or 10 seconds...I don't care about teh interval...al I want to know is how to get from acceleration of 12mph in one second to horsepower value for that tme

If you know the acceleration and mass, you know the force. If you know the force and distance, you know the work. If you know the work and time, you know the power. And 1hp is about 750W (I don't remember the exact conversion). Does any of that help?

 

[buffordboy23]

Acceleration of the car is caused by a force. When the force acts over a certain distance it does work. If you assume that the acceleration is constant, then the force is constant: force = mass x acceleration. When you accelerate your car and it moves over a distance d, work is done: Work = force x distance and has units of joules (energy). Now, it takes your car some amount of time to traverse this distance. Power is the rate at which work is applied: power = work / time and has units of joules per second (or watts). Horsepower conversion: 1 hp = 750 watts (approx.).

Don't forget that the car has to overcome numerous frictional forces so this may complicate your analysis.

Does this give you a better idea?

 

[swraman]

I did this for a math experiment to test horsepower of cars and compare them to manufacturers data.
I fitted a curve to the data as a function of time, then used that as position function x(t). from there there are many ways to get to power as a function of time; remember a car's power changes with time (it is not constant).

 

[soundengineer]

I tried to a car analysis at one time. Here is a link with a lot of formulas:

http://www.rdrop.com/~/larry/download/formulas.pdf

See if this helps. I couldn't see your car data.

I re-did the URL
you should be able to see it now...I forgot to put it in share mode

 

[soundengineer]

Acceleration of the car is caused by a force. When the force acts over a certain distance it does work. If you assume that the acceleration is constant, then the force is constant: force = mass x acceleration. When you accelerate your car and it moves over a distance d, work is done: Work = force x distance and has units of joules (energy). Now, it takes your car some amount of time to traverse this distance. Power is the rate at which work is applied: power = work / time and has units of joules per second (or watts). Horsepower conversion: 1 hp = 750 watts (approx.).

Don't forget that the car has to overcome numerous frictional forces so this may complicate your analysis.

Does this give you a better idea?

I get this...
I just have a hard time with understanding the units
force = mass x acceleration
what units are force?
is mass LBS or KG
what is the acceleration unit?

so work(joules) = (mass x acceleration) x distance

how can I get the distance? tire diameter math and speed correct?
and does that need to be in inches? feet? meters?

so...Power(watts) =((mass x acceleration) x distance) / time(in seconds?)
and that whole thing...
watts * 0.00134102209 = Horsepower
or watts / 745.699872 = Horsepoweram I correct in the math formula??
if yes..then I just need help with the units of measure being used in my variables

 

[Saladsamurai]

Force should be in Newtons or pound-force. You need to get the mass of your car instead of weight. I would go with metric units for now. Covert your weight to Newtons and then divide by local gravity 9.81 m/s² should be fine.

 

[soundengineer]

Force should be in Newtons or pound-force. You need to get the mass of your car instead of weight. I would go with metric units for now. Covert your weight to Newtons and then divide by local gravity 9.81 m/s² should be fine.

so my mass should be
3400 * 4.4482216 = 15123.95344 Newtons / 9.81 = 1541.6874046890927624872579001019
rounded = 1541.6874 (what unit?)

and what about the acceleration part...
what formula is my acceleration? and what are my units for acceleration?

 

[Saladsamurai]

mass=kgs
acceleration should be in meters per second squared. But you do not have acceleration, you have the vehicles speed (or velocity) at various times.

You need to come up with a formula or function that relates the sample velocities to time.

 

[soundengineer]

mass=kgs
acceleration should be in meters per second squared. But you do not have acceleration, you have the vehicles speed (or velocity) at various times.

You need to come up with a formula or function that relates the sample velocities to time.

so could I have just done

1 pound = 0.45359237 kilograms (google)
and taken 3400lbs * 0.45359237 = 1542.214058 kilograms
even though it doesn't quite match up to the previous math 1541.6874 kg?

as far as the acceleration...
difference in velocity over difference in time ? correct??
this formula just popped back in my head...
so (dV2-dV1)/(dT2-dT2)
velocity in meters/second and time in seconds
which gives me the acceleration in m/s^2


so...Power(watts) =(([mass_in_kg] x [(dV2-dV1)/(dT2-dT2)]) x [meters_traveled]) / time(in seconds)

 

[Saladsamurai]

Looks pretty good to me. (dV2-dV1)/(dT2-dT2) will get you the average acceleration and hence the average force and hence the average power.

You might be able to get a better approximation of acceleration by plotting a portion of your data in excel and finding a regression line and then using that to find the work done. But, that is only if you want to.

 

[soundengineer]

Looks pretty good to me. (dV2-dV1)/(dT2-dT2) will get you the average acceleration and hence the average force and hence the average power.

You might be able to get a better approximation of acceleration by plotting a portion of your data in excel and finding a regression line and then using that to find the work done. But, that is only if you want to.

I was planning on that :)
I have plans on using the data to solving for horsepower in vehicles at the dragstrip...
lets me know if the vehicle is running it tip top shape or if we need to adjust some things to get a little more power out of it..
we know what it does at its best...and we know what to adjust to compensate for various weather/climate conditions to get back to that...we've only figured that stuff out from the dyno...if we can come up with a dyno on the dragstrip then we can run a better race

one thing I don't get
Power(watts) =(([mass_in_kg] x [(dV2-dV1)/(dT2-dT2)]) x [meters_traveled]) / time(in seconds)

what is my bold type time in seconds?
where do I get that value?

 

[Saladsamurai]

I believe that should be the same time as used in the formula for acceleration. Think about it, you want to know how much Work (Force*displacement) this thing does PER second (Power). So if your force was calculated over a certain time interval (and then work with a corresponding distance interval) than you need to divide that work by THAT time interval to get Power over that interval.

 

[soundengineer]

I believe that should be the same time as used in the formula for acceleration. Think about it, you want to know how much Work (Force*displacement) this thing does PER second (Power). So if your force was calculated over a certain time interval (and then work with a corresponding distance interval) than you need to divide that work by THAT time interval to get Power over that interval.

so a recap to make sure this is right

((([mass_in_kg] x [(dV2-dV1)/(dT2-dT1)]) x [meters_traveled]) / [(dT2-dT1)seconds])* 0.00134102209 = Horsepower

Torque = (Horsepower x 5252)/RPM

then I can plot them both in excel and do some comparisons :)

 

[soundengineer]

ok...so I think I did some bad math somewhere...
seconds/rpm/mph/gear/dv/dt/distance/HP
7.52 3551 22.37 2.922 0.62 0.07 0.65 0.83
7.65 3605 22.99 2.922 0.62 0.13 1.34 1.71
obviously my HP math is wrong somewhere


=(((3400*0.45359237)*(DV/DT)*Distance)*DT)*0.00134102209


I also re-updated the Data in the google documents page
you are looking at data in line 10/11

 

[Saladsamurai]

I am confused by your data chart. The "distance traveled" column... what exactly is that? It obviously is not the Total distance traveled at that time... is it the distance traveled between each interval?

 

[soundengineer]

I am confused by your data chart. The "distance traveled" column... what exactly is that? It obviously is not the Total distance traveled at that time... is it the distance traveled between each interval?

yes distance traveled for a given dT2-dT1

is that the correct one to use or is that my error?

 

[Kizaru]

For finding the acceleration, why are you using mph for velocity? You should just convert to m/s.

Force = N = kg * m/s^2
Work = J = N*m (not to be confused with torque's N*m though)
Watt = W = J/s

This is the true beauty of SI units :)
You should convert everything to SI first, then after you find the wattage, convert to HP.

Your formula here:
=(((3400*0.45359237)*(DV/DT)*Distance)*DT)*0.00134102209
Is WRONG! If DT is change in time, it should be division not multiplication.

Which makes sense, does it not? Your HP is coming to be really low because you're multiplying some number by something like 0.1 (which is the same as dividing by 10). If you divide some number by something like 0.1 (which is the same as multiplying it by 10), you'll get a larger number.

 

[soundengineer]

For finding the acceleration, why are you using mph for velocity? You should just convert to m/s.

Force = N = kg * m/s^2
Work = J = N*m (not to be confused with torque's N*m though)
Watt = W = J/s

This is the true beauty of SI units :)
You should convert everything to SI first, then after you find the wattage, convert to HP.

Your formula here:
=(((3400*0.45359237)*(DV/DT)*Distance)*DT)*0.00134102209
Is WRONG! If DT is change in time, it should be division not multiplication.

Which makes sense, does it not? Your HP is coming to be really low because you're multiplying some number by something like 0.1 (which is the same as dividing by 10). If you divide some number by something like 0.1 (which is the same as multiplying it by 10), you'll get a larger number.

so in my worksheet I have
=(((3400*0.45359237)*(F3/G3)*H3)*G3)*0.00134102209
so I messed up the math...lol...
now I corrected it...it looks more correct than it did...
so I can go to excel and do some magic and do some longer stretches there...make it over 1 second or 2 seconds and smooth out the data instead of per sample

 

[soundengineer]

ok...so new worksheet
real data...

http://www.audiohelix.com/physics/HP%20TQ.xls"

the vehicle in question was Approximately 450 horsepower and 395 Torque measured on a chassis dyno(power thru the tires...no wind/friction dynamics to get in the way)

somewhere my math is obviously not correct..I don't know where and I need some help

In my graph I'm seeing 650hp..which is way over the mark

 

[Kizaru]

Using the spreadsheet in the first post, I made some columns where I converted mph to m/s using google's conversion rate (I googled 1mph in m/s). I made a column for acceleration, force, work, and two for power (one in W and one in HP). For the data, there were only two high points (382 and 426 HP). The rest were below 200.

Coincidentally, all of my HP values were 0.45 of the "raw HP" values and 1.31 of the "gear adjusted" values. This leads me to believe you messed up a conversion somewhere.

I think I see your mistake. You didn't convert mph to m/s. Your "dv" column is simply mph (specifically, you subtracted two cells that were both in mph only). One mph is greater than a m/s, which explains, which your acceleration comes out greater, yielding a higher force, work, and power. In the formula for dv, you simply need to add conversion rate for mph to m/s.

EDIT: I just changed my acceleration column and used your dv values instead of my converted values. These match your "raw HP" values, so there lies your mistake. I also pointed this out in my previous point that you were still using mph for velocity instead of m/s :)

 

[soundengineer]

i corrected my math in the google docs example...
Seems to make sense now... Not sure if i need to use the gear corrected one or not because i don't have any dyno data for that vehicle...I also realized that my excel spreadsheet didnt have gear correction on it... Once i did math for he gear ratio then it all got way way closer...
Its still not quite in line with the dyno #'s... But its useable data and i can work with it
Also its possible that the dyno is doing some things that arent quite the same as the math on paper and adding a correction factor to it.. I know i can go from one dyno to another and see different results ... Even between the same brand and runs done in exactly the same weather conditions on the same day just an hour apart from one another...