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Whats my best formula to use to calculate Horsepower or Torque from acceleration data

  1. Jan 29, 2009 #1
    I need to know what the "BEST" formula for me to use is...
    and I actually have 5 decimal places on all this data listed below..

    the data I have is in samples taken in real time..

    I need to come up with a way to calculate either the Torque or the Horsepower at the wheels...I can derive one from th eother after I get to one of them...
    I also know my wheel size/diameter

    Code (Text):

    Frame | Time |  Engine RPM (SAE) rpm    | Vehicle Speed (SAE) mph |  Throttle Position (SAE) % |    Trans Calculated Gear Ratio  |  Air Fuel Ratio Commanded Lo Res afr

    409 48:57.3 4062    50  56  1   14.6
    410 48:57.3 4097    50  57  1   12.7
    411 48:57.4 4136    50  58  1   12.7
    412 48:57.4 4157    50  59  1   12.7
    413 48:57.4 4186    50  59  1   12.7
    414 48:57.4 4202    50  59  1   12.7
    415 48:57.5 4226    51  59  1   12.7
    416 48:57.5 4252    50  59  1   12.7
    417 48:57.5 4260    50  59  1   12.7
    418 48:57.6 4276    50  59  1   12.7
    419 48:57.6 4273    50  59  1   12.7
    420 48:57.6 4273    50  59  1   12.7
    421 48:57.6 4272    50  59  1   12.7
    422 48:57.7 4274    50  60  1   12.7
    423 48:57.7 4287    50  60  1   12.7
    424 48:57.7 4286    50  63  1   12.7
    425 48:57.7 4292    50  64  1   12.7
    426 48:57.8 4308    50  65  1   12.7
    427 48:57.8 4322    50  66  1   12.7
    428 48:57.8 4330    50  67  1   12.7
    429 48:57.8 4343    50  70  1   12.7
    430 48:57.9 4356    50  77  1   12.7
    431 48:57.9 4428    51  100 1   12.7
    432 48:58.0 4446    51  100 1   12.7
    433 48:58.0 4469    51  100 1   12.7
    434 48:58.0 4488    51  100 1   12.7
    435 48:58.0 4505    51  100 1   12.7
    436 48:58.0 4528    51  100 1   12.7
    437 48:58.1 4539    52  100 1   12.7
    438 48:58.1 4549    51  100 1   12.7
    439 48:58.1 4558    52  100 1   12.7
    440 48:58.2 4572    51  100 1   12.7
    441 48:58.2 4588    51  100 1   12.7
    442 48:58.2 4592    52  100 1   12.7
    443 48:58.3 4598    51  100 1   12.7
    444 48:58.3 4603    52  100 1   12.7
    445 48:58.3 4613    52  100 1   12.7
    446 48:58.3 4619    51  100 1   12.7
    447 48:58.4 4619    51  100 1   12.7
    448 48:58.4 4623    51  100 1   12.7
    449 48:58.4 4620    51  100 1   12.7
    450 48:58.4 4626    51  100 1   12.7
    451 48:58.5 4626    51  100 1   12.7
    452 48:58.5 4627    51  100 1   12.7
    453 48:58.5 4626    51  100 1   12.7
    454 48:58.5 4629    51  100 1   12.7
    455 48:58.6 4638    51  100 1   12.7
    456 48:58.6 4638    51  100 1   12.7
    457 48:58.6 4642    51  100 1   12.7
    458 48:58.6 4636    51  100 1   12.7
    459 48:58.7 4638    51  100 1   12.7
    460 48:58.7 4633    51  100 1   12.7
    461 48:58.7 4633    51  100 1   12.7
    462 48:58.7 4633    51  100 1   12.7
    463 48:58.7 4634    51  100 1   12.7
    464 48:58.8 4630    51  100 1   12.7
    465 48:58.8 4629    51  100 1   12.7
    466 48:58.8 4636    51  100 1   12.7
    467 48:58.8 4633    51  100 1   12.7
    468 48:58.9 4642    51  100 1   12.7
    469 48:58.9 4636    51  100 1   12.7
    470 48:58.9 4639    51  100 1   12.7
    471 48:58.9 4644    51  100 1   12.7
    472 48:59.0 4644    51  100 1   12.7
    473 48:59.0 4647    51  100 1   12.7
    474 48:59.0 4639    52  100 1   12.7
    475 48:59.0 4636    52  100 1   12.7
    476 48:59.1 4644    52  100 1   12.7
    477 48:59.1 4643    52  100 1   12.7
    478 48:59.1 4647    52  100 1   12.7
    479 48:59.1 4649    52  100 1   12.7
    480 48:59.2 4663    53  100 1   12.7
    481 48:59.2 4672    53  100 1   12.7
    482 48:59.2 4679    53  100 1   12.7
    483 48:59.2 4688    54  100 1   12.7
    484 48:59.3 4697    54  100 1   12.7
    485 48:59.3 4698    54  100 1   12.7
    486 48:59.3 4710    55  100 1   12.7
    487 48:59.3 4712    55  100 1   12.7
    488 48:59.4 4718    55  100 1   12.7
    489 48:59.4 4726    55  100 1   12.7
    490 48:59.4 4731    56  100 1   12.7
    491 48:59.5 4736    56  100 1   12.7
    492 48:59.5 4754    57  100 1   12.7
    493 48:59.5 4760    57  100 1   12.7
    494 48:59.5 4766    57  100 1   12.7
    495 48:59.6 4772    57  100 1   12.7
    496 48:59.6 4785    58  100 1   12.7
    497 48:59.6 4790    58  100 1   12.7
    498 48:59.7 4800    58  100 1   12.7
    499 48:59.7 4807    58  100 1   12.7
    500 48:59.7 4813    58  100 1   12.7
    501 48:59.7 4820    59  100 1   12.7
    502 48:59.7 4824    59  100 1   12.7
    503 48:59.8 4832    59  100 1   12.7
    504 48:59.8 4835    60  100 1   12.7
    505 48:59.8 4842    60  100 1   12.7
    506 48:59.8 4850    60  100 1   12.7
    507 48:59.9 4850    60  100 1   12.7
    508 48:59.9 4856    61  100 1   12.7
    509 48:59.9 4860    61  100 1   12.7
    510 48:59.9 4864    61  100 1   12.7
    511 49:00.0 4871    62  100 1   12.7
    512 49:00.0 4882    62  100 1   12.7
    513 49:00.0 4890    62  100 1   12.7
    514 49:00.0 4894    62  100 1   12.7
    515 49:00.1 4901    62  100 1   12.7
    516 49:00.1 4914    63  100 1   12.7
    517 49:00.1 4915    63  100 1   12.7
    518 49:00.1 4927    63  100 1   12.7
    519 49:00.2 4930    63  100 1   12.7
    520 49:00.2 4936    63  100 1   12.7
    521 49:00.2 4944    64  100 1   12.7
    522 49:00.3 4954    64  100 1   12.7
    523 49:00.3 4959    65  100 1   12.7
    524 49:00.3 4967    65  100 1   12.7
    525 49:00.3 4970    65  100 1   12.7
    526 49:00.3 4977    65  100 1   12.7
    527 49:00.4 4980    65  100 1   12.7
    528 49:00.4 4982    66  100 1   12.7
    529 49:00.4 4988    66  100 1   12.7
    530 49:00.5 4998    66  100 1   12.7
    531 49:00.5 5000    66  100 1   12.7
    532 49:00.5 5003    67  100 1   12.7
    533 49:00.5 5010    67  100 1   12.7
    534 49:00.6 5015    67  100 1   12.7
    535 49:00.6 5025    68  100 1   12.7
    536 49:00.6 5023    68  100 1   12.7
    537 49:00.6 5025    68  100 1   12.7
    538 49:00.7 5030    68  100 1   12.7
    539 49:00.7 5035    68  100 1   12.7
    540 49:00.7 5045    69  100 1   12.7
    541 49:00.7 5050    69  100 1   12.7
    542 49:00.8 5054    69  100 1   12.7
    543 49:00.8 5054    70  100 1   12.7
    544 49:00.8 5054    70  100 1   12.7
    545 49:00.8 5062    70  100 1   12.7
    546 49:00.9 5064    70  100 1   12.7
    547 49:00.9 5064    70  100 1   12.7
    548 49:00.9 5081    70  100 1   12.7
    549 49:00.9 5084    71  100 1   12.7
    550 49:01.0 5093    71  100 1   12.7
    551 49:01.0 5092    71  100 1   12.7
    552 49:01.0 5095    71  100 1   12.7
    553 49:01.1 5096    72  100 1   12.7
    554 49:01.1 5100    72  100 1   12.7
    555 49:01.1 5104    73  100 1   12.7
    556 49:01.1 5110    73  100 1   12.7
    557 49:01.2 5114    73  100 1   12.7
    558 49:01.2 5121    73  100 1   12.7
    559 49:01.2 5130    73  100 1   12.7
    560 49:01.2 5128    74  100 1   12.7
    561 49:01.3 5128    74  100 1   12.7
    562 49:01.3 5138    75  100 1   12.7
    563 49:01.3 5156    75  100 1   12.7
    564 49:01.4 5160    75  100 1   12.7
    565 49:01.4 5151    75  100 1   12.7
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    567 49:01.4 5167    75  100 1   12.7
    568 49:01.5 5169    76  100 1   12.7
    569 49:01.5 5172    76  100 1   12.7
    570 49:01.5 5179    76  100 1   12.7
    571 49:01.6 5183    76  100 1   12.7
    572 49:01.6 5194    77  100 1   12.7
    573 49:01.6 5188    77  100 1   12.7
    574 49:01.6 5197    77  100 1   12.7
    575 49:01.7 5197    78  100 1   12.7
    576 49:01.7 5208    78  100 1   12.7
    577 49:01.7 5214    78  100 1   12.7
    578 49:01.7 5210    78  100 1   12.7
    579 49:01.8 5212    78  100 1   12.7
    580 49:01.8 5222    79  100 1   12.7
    581 49:01.8 5228    79  100 1   12.7
    582 49:01.8 5228    79  100 1   12.7
    583 49:01.9 5232    80  100 1   12.7
    584 49:01.9 5248    80  100 1   12.7
    585 49:01.9 5241    80  100 1   12.7
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    587 49:02.0 5256    80  100 1   12.7
    588 49:02.0 5272    81  100 1   12.7
    589 49:02.0 5268    81  100 1   12.7
    590 49:02.0 5272    81  100 1   12.7
    591 49:02.0 5282    81  100 1   12.7
    592 49:02.1 5287    81  100 1   12.7
    593 49:02.1 5293    82  100 1   12.7
    594 49:02.1 5296    82  100 1   12.7
    595 49:02.2 5302    83  100 1   12.7
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    600 49:02.3 5334    84  100 1   12.7
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    608 49:02.5 5366    86  100 1   12.7
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    611 49:02.6 5386    86  100 1   12.7
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    649 49:03.6 5641    96  100 1   12.7
    650 49:03.6 5656    96  100 1   12.7
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  2. jcsd
  3. Jan 29, 2009 #2

    rcgldr

    User Avatar
    Homework Helper

    Re: whats my best formula to use to calculate Horsepower or Torque from acceleration

    You need to know the weight of the car. You also need to measure the rate of deceleration with the clutch depressed, which will let you calcuate the drag factors. You'll probably need to do a curve fit for the drag factors (aerodynamic, drivetrain, rolling resistance).

    Given that, then you can determine the net force (lbs) during each frame interval by the rate of acceleration (ft / sec^2) times mass (slugs) of the car. The force at the driven tires equals the net force + drag force. The power at the rear tires equals this force times speed.

    To determing horsepower (regardless of gearing)

    (power/horsepower) = force (lbs) x speed (mph) / 375 (conversion factor)
     
  4. Jan 29, 2009 #3
    Re: whats my best formula to use to calculate Horsepower or Torque from acceleration

    you lost me a little bit there...
    so force = ft/sec^2 x Mass(which I can calculate that knowing the lbs.....)
    then that result x MPH
    what is the 375 from?I need to know exactly where that # comes from...

    I'm not worried about the deceleration just yet....
     
  5. Jan 29, 2009 #4
  6. Jan 29, 2009 #5

    rcgldr

    User Avatar
    Homework Helper

    Re: whats my best formula to use to calculate Horsepower or Torque from acceleration

    The link above explains this but I used 550 ft lb / sec for the unit of horsepower:

    power / horsepower = (1 sec) / (550 ft lb) = (1 sec / 550 ft) (1 / lb)

    power = force (lb) x speed (1 mile / hour) = force x speed ( 1 lb mile / hour) =
    power = force x speed (1 lb) (1 mile) (1 / hour) (5280 ft / mile) (hour / 3600 sec) =
    power = force x speed (1 lb 5280 ft / 3600 sec)

    power / horsepower = force x speed (1 lb 5280 ft / 3600 sec) (1 sec / 550 ft) (1 / lb)
    power / horsepower = force x speed (1 / 375)

    Note that dynos can measure power from force and speed without ever knowing engine rpm, torque, or gearing. By including rpm information, then the dyno can calculate engine torque after losses, and the effective gearing in terms of linear speed versus rpm. Actual gearing information or tire size will give the rest of the data, although the effective radius of a tire under load is smaller than the non-loaded radius.
     
    Last edited: Jan 29, 2009
  7. Nov 5, 2009 #6
    Re: whats my best formula to use to calculate Horsepower or Torque from acceleration

    Would it be correct if I then say :

    power = force * speed

    power = weight * acceleration * (vo + (acceleration * time) ??

    lets say that my accelerometer tells me that the acceleration at this moment is 5,77 m/s^2, and that time since last reading is 0,222 seconds - given a weight of the car at 1500 kilograms. and that v0 = 0

    power(w) = 1500 * 5,77 * 5,77 * 0,222 ?
     
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