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

soundengineer

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:

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
566	49:01.4	5154	75	100	1	12.7
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
586	49:01.9	5248	80	100	1	12.7
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
596	49:02.2	5312	83	100	1	12.7
597	49:02.2	5326	83	100	1	12.7
598	49:02.2	5326	83	100	1	12.7
599	49:02.3	5323	83	100	1	12.7
600	49:02.3	5334	84	100	1	12.7
601	49:02.3	5334	84	100	1	12.7
602	49:02.4	5344	84	100	1	12.7
603	49:02.4	5359	85	100	1	12.7
604	49:02.4	5359	85	100	1	12.7
605	49:02.4	5353	85	100	1	12.7
606	49:02.5	5361	85	100	1	12.7
607	49:02.5	5374	85	100	1	12.7
608	49:02.5	5366	86	100	1	12.7
609	49:02.5	5372	86	100	1	12.7
610	49:02.6	5380	86	100	1	12.7
611	49:02.6	5386	86	100	1	12.7
612	49:02.6	5397	86	100	1	12.7
613	49:02.6	5394	87	100	1	12.7
614	49:02.7	5401	87	100	1	12.7
615	49:02.7	5411	87	100	1	12.7
616	49:02.7	5425	88	100	1	12.7
617	49:02.7	5419	88	100	1	12.7
618	49:02.7	5428	88	100	1	12.7
619	49:02.8	5430	88	100	1	12.7
620	49:02.8	5440	88	100	1	12.7
621	49:02.8	5448	88	100	1	12.7
622	49:02.8	5442	89	100	1	12.7
623	49:02.9	5454	89	100	1	12.7
624	49:02.9	5466	89	100	1	12.7
625	49:02.9	5462	89	100	1	12.7
626	49:03.0	5470	89	100	1	12.7
627	49:03.0	5488	90	100	1	12.7
628	49:03.0	5486	90	100	1	12.7
629	49:03.0	5502	91	100	1	12.7
630	49:03.1	5514	91	100	1	12.7
631	49:03.1	5512	91	100	1	12.7
632	49:03.1	5520	91	100	1	12.7
633	49:03.2	5525	91	100	1	12.7
634	49:03.2	5541	92	100	1	12.7
635	49:03.2	5535	92	100	1	12.7
636	49:03.2	5551	93	100	1	12.7
637	49:03.2	5557	93	100	1	12.7
638	49:03.3	5555	93	100	1	12.7
639	49:03.3	5564	93	100	1	12.7
640	49:03.3	5578	93	100	1	12.7
641	49:03.3	5590	93	100	1	12.7
642	49:03.4	5582	94	100	1	12.7
643	49:03.4	5601	94	100	1	12.7
644	49:03.4	5599	94	100	1	12.7
645	49:03.5	5610	94	100	1	12.7
646	49:03.5	5632	95	100	1	12.7
647	49:03.5	5620	95	100	1	12.7
648	49:03.5	5639	95	100	1	12.7
649	49:03.6	5641	96	100	1	12.7
650	49:03.6	5656	96	100	1	12.7
651	49:03.6	5654	96	100	1	12.7
652	49:03.6	5675	96	100	1	12.7
653	49:03.7	5666	96	100	1	12.7
654	49:03.7	5686	96	100	1	12.7
655	49:03.7	5690	97	100	1	12.7
656	49:03.8	5701	97	100	1	12.7
657	49:03.8	5718	98	100	1	12.7
658	49:03.8	5712	98	100	1	12.7
659	49:03.8	5738	98	100	1	12.7
660	49:03.8	5736	98	100	1	12.7
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662	49:03.9	5769	98	100	1	12.7
663	49:03.9	5771	99	100	1	12.7
664	49:04.0	5767	99	100	1	12.7
665	49:04.0	5791	100	100	1	12.7
666	49:04.0	5820	100	100	1	12.7
667	49:04.1	5833	100	100	1	12.7
668	49:04.1	5835	101	100	1	12.7
669	49:04.1	5844	101	100	1	12.7
670	49:04.2	5867	101	100	1	12.7
671	49:04.2	5881	101	100	1	12.7
672	49:04.2	5890	101	100	1	12.7
673	49:04.2	5890	102	100	1	12.7
674	49:04.3	5913	102	100	1	12.7
675	49:04.3	5925	103	100	1	12.7
676	49:04.3	5932	103	100	1	12.7
677	49:04.4	5937	103	100	1	12.7
678	49:04.4	5963	103	100	1	12.7
679	49:04.4	5958	103	100	1	12.7
680	49:04.4	5968	104	100	1	12.7
681	49:04.4	5979	104	100	1	12.7
682	49:04.5	6001	104	100	1	12.7
683	49:04.5	5996	104	100	1	12.7
684	49:04.5	6008	104	100	1	12.7
685	49:04.6	6020	104	100	1	12.7
686	49:04.6	6040	105	100	1	12.7
687	49:04.6	6037	105	100	1	12.7
688	49:04.6	6047	105	100	1	12.7
689	49:04.6	6054	106	100	1	12.7
690	49:04.7	6081	106	100	1	12.7
691	49:04.7	6079	106	100	1	12.7
692	49:04.7	6091	106	100	1	12.7
693	49:04.8	6101	106	100	1	12.7
694	49:04.8	6116	107	100	1	12.7
695	49:04.8	6128	107	100	1	12.7
696	49:04.8	6131	108	100	1	12.7
697	49:04.9	6144	108	100	1	12.7
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732	49:05.8	6467	115	100	1	12.7
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738	49:06.0	6517	116	100	1	12.7
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740	49:06.0	6534	116	100	1	12.7
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751	49:06.3	6392	116	100	1	12.7
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760	49:06.5	6403	117	100	1	12.7

rcgldr

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)

soundengineer

Quote by Jeff Reid

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)

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....

nucleus

This site explains it pretty good. See also the part on Aero Drag
http://craig.backfire.ca/pages/autos/horsepower

rcgldr

Quote by Jeff Reid

(power/horsepower) = force (lbs) x speed (mph) / 375 (conversion factor)

Quote by soundengineer

What is the 375 from?

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.

andpe

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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nucleus	whats my best formula to use to calculate Horsepower or Torque from acceleration data This site explains it pretty good. See also the part on Aero Drag http://craig.backfire.ca/pages/autos/horsepower

andpe	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 ?