Mathematically-based 0-60 mph calculator
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
Mathematically-based 0-60 mph calculator
Link to Excel spreadsheet is here.
I'm posting this in C6 tech/perf because I'm guessing that there are more folks in this group who like to race their Vettes than in other groups.
Like many of you here, I enjoy drag racing my Vette. One aspect of drag racing that I've always wondered about was how to convert data from racing slips to 0-60 MPH data. This interest is because many people who don't race have a better handle on 0-60 times as a measure of performance than quarter or eighth mile times.
If you don't want to read the rest of this post and instead just play with the Excel spreadsheet, you can download it here. Note that the spreadsheet is locked - you can only enter data for the 60, 330, and 1/8 mile times into the table on the left. Now look at the table on the right and see your 0-60 mph time and distance.
WARNING - CALCULUS FOLLOWS
Last weekend I set about to tackle the problem mathematically (I'm an engineer, so that's how I like to think). The initial acceleration is non-linear, and is much greater during the initial launch than it is during most of the run down the track. Still, the movement of the car is basically 'smooth' in that the position of the car as a function of time is inherently 'smooth', or in mathematical terms, has a continuous first derivative.
The point in space where the car crosses the 60 MPH velocity is somewhere in the first eighth mile (assuming normal track acceleration). Therefore, one needs only several datapoints bounding the 60 MPH point. A typical timeslip has this info: the 60', 330', and 1/8 mile times, as well as the 1/8 mile speed. We'll start out with the time data only, and come back to the 1/8 speed later.
We also have one more datapoint: at t=0, the position of the car is 0 feet. So, we have a total of 4 datapoints: 0, 60, 330, and 660 feet. We can fit a smooth third-order polynomial perfectly to these four points, and I use this polynomial to model the position of the car with time. The polynomial has the following form:
d = A*t^3 + B*t^2 + C*t + D
Where d = distance in feet,
t = time in seconds, and
A, B, C, and D are the constant coefficients to be fitted to the data.
Velocity is the first derivative of position with respect to time. Taking the derivative of the equation above, we have:
V = 3At^2 + 2Bt + C
The goal of this exercise is to find the time at which the velocity is exactly 60 MPH, or 88 ft/sec. We substitute 88 for the velocity in the equation above and have:
88 = 3At^2 + 2Bt + C
We can rearrange this equation to provide a familiar quadratic expression:
0 = 3At^2 + 2Bt + (C-88)
The solution to the quadratic equation is familiar to all math students:
Only one root is important here, and it is easily found by trial-and-error.
We now just need to substitute for a, b, and c the terms from the equation above, and voila: a solution for the problem of the 0-60 time.
I put all this into the Excel spreadsheet above, and you can see how it graphs the modeled position of the car as a function of time. From the third-order polynomial equation, it calculates the derivatives, and from them, the time to reach a velocity of 60 MPH. This is shown in the table at the top right.
To use the spreadsheet, simply enter the times for 60, 330, and 660 feet (1/8 mile) into the table on the left and see the calculated 60 MPH time. The graph has a big red triangle on the 60 MPH spot.
There's a good way to check the accuracy of this procedure. Remember the 1/8 MPH we looked at but never used? Here's where it comes in. From the polynomial model, we can determine the velocity at the quarter-mile time. The table on the right shows the estimated eighth mile speed. Compare that value to your timeslip. If they are pretty close (within about 1-2 MPH) then the model is a good fit and you can rely on the 0-60 time. If they differ by more than that, your acceleration was variable - perhaps because of wheel spin, or maybe a missed shift.
Finally, there is a 0-60 calculator on the Wallace Racing site. This calculator uses only the eighth mile time and speed to estimate the 0-60 times. I compared dozens of my timeslips using both methods, and they generally agreed to within a few percent. Pretty good for an engineering estimate.
Play around with the spreadsheet and let me know if you find it useful. From a mathematical perspective, i believe it to be superior to the Wallace method in that it uses more data to model the acceleration.
Here's a view of the spreadsheet and its results for my car. As it is said, YMMV.
I'm posting this in C6 tech/perf because I'm guessing that there are more folks in this group who like to race their Vettes than in other groups.
Like many of you here, I enjoy drag racing my Vette. One aspect of drag racing that I've always wondered about was how to convert data from racing slips to 0-60 MPH data. This interest is because many people who don't race have a better handle on 0-60 times as a measure of performance than quarter or eighth mile times.
If you don't want to read the rest of this post and instead just play with the Excel spreadsheet, you can download it here. Note that the spreadsheet is locked - you can only enter data for the 60, 330, and 1/8 mile times into the table on the left. Now look at the table on the right and see your 0-60 mph time and distance.
WARNING - CALCULUS FOLLOWS
Last weekend I set about to tackle the problem mathematically (I'm an engineer, so that's how I like to think). The initial acceleration is non-linear, and is much greater during the initial launch than it is during most of the run down the track. Still, the movement of the car is basically 'smooth' in that the position of the car as a function of time is inherently 'smooth', or in mathematical terms, has a continuous first derivative.
The point in space where the car crosses the 60 MPH velocity is somewhere in the first eighth mile (assuming normal track acceleration). Therefore, one needs only several datapoints bounding the 60 MPH point. A typical timeslip has this info: the 60', 330', and 1/8 mile times, as well as the 1/8 mile speed. We'll start out with the time data only, and come back to the 1/8 speed later.
We also have one more datapoint: at t=0, the position of the car is 0 feet. So, we have a total of 4 datapoints: 0, 60, 330, and 660 feet. We can fit a smooth third-order polynomial perfectly to these four points, and I use this polynomial to model the position of the car with time. The polynomial has the following form:
d = A*t^3 + B*t^2 + C*t + D
Where d = distance in feet,
t = time in seconds, and
A, B, C, and D are the constant coefficients to be fitted to the data.
Velocity is the first derivative of position with respect to time. Taking the derivative of the equation above, we have:
V = 3At^2 + 2Bt + C
The goal of this exercise is to find the time at which the velocity is exactly 60 MPH, or 88 ft/sec. We substitute 88 for the velocity in the equation above and have:
88 = 3At^2 + 2Bt + C
We can rearrange this equation to provide a familiar quadratic expression:
0 = 3At^2 + 2Bt + (C-88)
The solution to the quadratic equation is familiar to all math students:
Only one root is important here, and it is easily found by trial-and-error.
We now just need to substitute for a, b, and c the terms from the equation above, and voila: a solution for the problem of the 0-60 time.
I put all this into the Excel spreadsheet above, and you can see how it graphs the modeled position of the car as a function of time. From the third-order polynomial equation, it calculates the derivatives, and from them, the time to reach a velocity of 60 MPH. This is shown in the table at the top right.
To use the spreadsheet, simply enter the times for 60, 330, and 660 feet (1/8 mile) into the table on the left and see the calculated 60 MPH time. The graph has a big red triangle on the 60 MPH spot.
There's a good way to check the accuracy of this procedure. Remember the 1/8 MPH we looked at but never used? Here's where it comes in. From the polynomial model, we can determine the velocity at the quarter-mile time. The table on the right shows the estimated eighth mile speed. Compare that value to your timeslip. If they are pretty close (within about 1-2 MPH) then the model is a good fit and you can rely on the 0-60 time. If they differ by more than that, your acceleration was variable - perhaps because of wheel spin, or maybe a missed shift.
Finally, there is a 0-60 calculator on the Wallace Racing site. This calculator uses only the eighth mile time and speed to estimate the 0-60 times. I compared dozens of my timeslips using both methods, and they generally agreed to within a few percent. Pretty good for an engineering estimate.
Play around with the spreadsheet and let me know if you find it useful. From a mathematical perspective, i believe it to be superior to the Wallace method in that it uses more data to model the acceleration.
Here's a view of the spreadsheet and its results for my car. As it is said, YMMV.
Last edited by MTVette; May 19, 2015 at 09:18 AM.
Le Mans Master
Joined: Oct 2007
Posts: 6,149
Likes: 11
From: Greater Detroit Metro MI, when I'm not travelling.
Well done! 
I've seen a few of those calculators before, but I don't think they are very accurate for cars experiencing a lot of wheelspin because once they hook up they go a lot faster than the initial acceleration would lead you to believe... It would be really need to use an accelerometer based meter (G-Tech for instance) and compare the results of that with your spredsheet.
I've seen a few of those calculators before, but I don't think they are very accurate for cars experiencing a lot of wheelspin because once they hook up they go a lot faster than the initial acceleration would lead you to believe... It would be really need to use an accelerometer based meter (G-Tech for instance) and compare the results of that with your spredsheet.
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
Thanks.
Even better than an accelerometer would be a direct link to the vehicle's speed sensor. That can be done with the older OBDI C4's, and probably even more easily with newer cars.
Even better than an accelerometer would be a direct link to the vehicle's speed sensor. That can be done with the older OBDI C4's, and probably even more easily with newer cars.
7th Gear
Joined: Oct 2008
Posts: 7
Likes: 0
the Polynomial or the Quadratic Curve Fit
is not quite accuate enough of a "Fit"
its close.... and a great estimate, and thanks for the accel.xls File !
even a Cubic Spline Fit is not going to be accurate enough to Model
every foot distance's real acceleration rate
here's an excerpt of a very old Acceleration Simluator i started about 20 years ago
as a DOS QuickBASIC program, i've converted to VB1.0 then finally to VB6.0 code
recently
i'm hoping to finally finish that Program before 2009
and it will be updated with Inputs for
660 Ft 's MPH
and
1320 Ft's MPH
as well as the new TopFuel + FunnyCar 1000 Feet MPH inputs
...the additional 660/1000/1320 feet's MPH inputs will greatly increase
the accuracy at every foot
60= 1.5740 40.7758
330= 4.6860 74.5102
660= 7.3440 91.9242
1000= 9.6725 105.2940
1320= 11.6663 112.5265
0 to 30 mph= 0.910
0 to 60 mph= 3.141
0 to 80 mph= 5.338
0 to 100 mph= 8.565
0 to 120 mph= 12.370
FT__ET_____MPH____GForce
50 1.4013 38.1818 0.6766
51 1.4191 38.4556 0.6728
52 1.4368 38.7259 0.6692
53 1.4544 38.9929 0.6656
54 1.4718 39.2566 0.6621
55 1.4891 39.5172 0.6587
56 1.5063 39.7747 0.6554
57 1.5234 40.0292 0.6521
58 1.5404 40.2809 0.6489
59 1.5572 40.5297 0.6458
60 1.5740 40.7758 0.6427
61 1.5907 41.0193 0.6397
62 1.6072 41.2601 0.6368
63 1.6237 41.4985 0.6339
64 1.6401 41.7344 0.6311
65 1.6564 41.9679 0.6284
66 1.6726 42.1991 0.6257
67 1.6887 42.4280 0.6230
68 1.7047 42.6546 0.6204
69 1.7207 42.8792 0.6178
70 1.7365 43.1016 0.6153
170 3.0608 59.1466 0.4755
171 3.0723 59.2692 0.4746
172 3.0838 59.3912 0.4738
173 3.0953 59.5127 0.4730
174 3.1067 59.6338 0.4721
175 3.1181 59.7544 0.4713
176 3.1295 59.8745 0.4705
177 3.1409 59.9942 0.4697
178 3.1523 60.1134 0.4689
179 3.1636 60.2322 0.4681
180 3.1749 60.3505 0.4673
330 4.6860 74.5102 0.3867
660 7.3440 93.3990 0.2991
1000 9.6725 105.2940 0.2460
1254 11.2664 111.8031 0.2180
1255 11.2725 111.8257 0.2179
1256 11.2786 111.8483 0.2178
1257 11.2847 111.8709 0.2177
1258 11.2908 111.8934 0.2176
1259 11.2969 111.9159 0.2175
1260 11.3030 111.9384 0.2174
1261 11.3091 111.9608 0.2173
1262 11.3152 111.9833 0.2172
1263 11.3213 112.0057 0.2171
1264 11.3273 112.0281 0.2170
1265 11.3334 112.0505 0.2169
1266 11.3395 112.0728 0.2168
1267 11.3456 112.0952 0.2167
1268 11.3517 112.1175 0.2166
1269 11.3578 112.1398 0.2165
1270 11.3638 112.1621 0.2164
1271 11.3699 112.1843 0.2163
1272 11.3760 112.2065 0.2162
1273 11.3821 112.2287 0.2161
1274 11.3881 112.2509 0.2160
1275 11.3942 112.2731 0.2159
1276 11.4003 112.2953 0.2158
1277 11.4064 112.3174 0.2157
1278 11.4124 112.3395 0.2156
1279 11.4185 112.3616 0.2155
1280 11.4246 112.3837 0.2154
1281 11.4306 112.4057 0.2153
1282 11.4367 112.4277 0.2152
1283 11.4428 112.4497 0.2151
1284 11.4488 112.4717 0.2150
1285 11.4549 112.4937 0.2149
1286 11.4609 112.5156 0.2149
1287 11.4670 112.5376 0.2148
1288 11.4731 112.5595 0.2147
1289 11.4791 112.5813 0.2146
1290 11.4852 112.6032 0.2145
1291 11.4912 112.6251 0.2144
1292 11.4973 112.6469 0.2143
1293 11.5033 112.6687 0.2142
1294 11.5094 112.6905 0.2141
1295 11.5154 112.7122 0.2140
1296 11.5215 112.7340 0.2139
1297 11.5275 112.7557 0.2138
1298 11.5336 112.7774 0.2137
1299 11.5396 112.7991 0.2136
1300 11.5457 112.8207 0.2135
1301 11.5517 112.8424 0.2134
1302 11.5577 112.8640 0.2133
1303 11.5638 112.8856 0.2132
1304 11.5698 112.9072 0.2131
1305 11.5759 112.9287 0.2130
1306 11.5819 112.9503 0.2129
1307 11.5879 112.9718 0.2128
1308 11.5940 112.9933 0.2128
1309 11.6000 113.0148 0.2127
1310 11.6060 113.0363 0.2126
1311 11.6121 113.0577 0.2125
1312 11.6181 113.0791 0.2124
1313 11.6241 113.1005 0.2123
1314 11.6302 113.1219 0.2122
1315 11.6362 113.1433 0.2121
1316 11.6422 113.1646 0.2120
1317 11.6482 113.1859 0.2119
1318 11.6543 113.2072 0.2118
1319 11.6603 113.2285 0.2117
1320 11.6663 113.2498 0.2116
is not quite accuate enough of a "Fit"
its close.... and a great estimate, and thanks for the accel.xls File !
even a Cubic Spline Fit is not going to be accurate enough to Model
every foot distance's real acceleration rate
here's an excerpt of a very old Acceleration Simluator i started about 20 years ago
as a DOS QuickBASIC program, i've converted to VB1.0 then finally to VB6.0 code
recently
i'm hoping to finally finish that Program before 2009
and it will be updated with Inputs for
660 Ft 's MPH
and
1320 Ft's MPH
as well as the new TopFuel + FunnyCar 1000 Feet MPH inputs
...the additional 660/1000/1320 feet's MPH inputs will greatly increase
the accuracy at every foot
60= 1.5740 40.7758
330= 4.6860 74.5102
660= 7.3440 91.9242
1000= 9.6725 105.2940
1320= 11.6663 112.5265
0 to 30 mph= 0.910
0 to 60 mph= 3.141
0 to 80 mph= 5.338
0 to 100 mph= 8.565
0 to 120 mph= 12.370
FT__ET_____MPH____GForce
50 1.4013 38.1818 0.6766
51 1.4191 38.4556 0.6728
52 1.4368 38.7259 0.6692
53 1.4544 38.9929 0.6656
54 1.4718 39.2566 0.6621
55 1.4891 39.5172 0.6587
56 1.5063 39.7747 0.6554
57 1.5234 40.0292 0.6521
58 1.5404 40.2809 0.6489
59 1.5572 40.5297 0.6458
60 1.5740 40.7758 0.6427
61 1.5907 41.0193 0.6397
62 1.6072 41.2601 0.6368
63 1.6237 41.4985 0.6339
64 1.6401 41.7344 0.6311
65 1.6564 41.9679 0.6284
66 1.6726 42.1991 0.6257
67 1.6887 42.4280 0.6230
68 1.7047 42.6546 0.6204
69 1.7207 42.8792 0.6178
70 1.7365 43.1016 0.6153
170 3.0608 59.1466 0.4755
171 3.0723 59.2692 0.4746
172 3.0838 59.3912 0.4738
173 3.0953 59.5127 0.4730
174 3.1067 59.6338 0.4721
175 3.1181 59.7544 0.4713
176 3.1295 59.8745 0.4705
177 3.1409 59.9942 0.4697
178 3.1523 60.1134 0.4689
179 3.1636 60.2322 0.4681
180 3.1749 60.3505 0.4673
330 4.6860 74.5102 0.3867
660 7.3440 93.3990 0.2991
1000 9.6725 105.2940 0.2460
1254 11.2664 111.8031 0.2180
1255 11.2725 111.8257 0.2179
1256 11.2786 111.8483 0.2178
1257 11.2847 111.8709 0.2177
1258 11.2908 111.8934 0.2176
1259 11.2969 111.9159 0.2175
1260 11.3030 111.9384 0.2174
1261 11.3091 111.9608 0.2173
1262 11.3152 111.9833 0.2172
1263 11.3213 112.0057 0.2171
1264 11.3273 112.0281 0.2170
1265 11.3334 112.0505 0.2169
1266 11.3395 112.0728 0.2168
1267 11.3456 112.0952 0.2167
1268 11.3517 112.1175 0.2166
1269 11.3578 112.1398 0.2165
1270 11.3638 112.1621 0.2164
1271 11.3699 112.1843 0.2163
1272 11.3760 112.2065 0.2162
1273 11.3821 112.2287 0.2161
1274 11.3881 112.2509 0.2160
1275 11.3942 112.2731 0.2159
1276 11.4003 112.2953 0.2158
1277 11.4064 112.3174 0.2157
1278 11.4124 112.3395 0.2156
1279 11.4185 112.3616 0.2155
1280 11.4246 112.3837 0.2154
1281 11.4306 112.4057 0.2153
1282 11.4367 112.4277 0.2152
1283 11.4428 112.4497 0.2151
1284 11.4488 112.4717 0.2150
1285 11.4549 112.4937 0.2149
1286 11.4609 112.5156 0.2149
1287 11.4670 112.5376 0.2148
1288 11.4731 112.5595 0.2147
1289 11.4791 112.5813 0.2146
1290 11.4852 112.6032 0.2145
1291 11.4912 112.6251 0.2144
1292 11.4973 112.6469 0.2143
1293 11.5033 112.6687 0.2142
1294 11.5094 112.6905 0.2141
1295 11.5154 112.7122 0.2140
1296 11.5215 112.7340 0.2139
1297 11.5275 112.7557 0.2138
1298 11.5336 112.7774 0.2137
1299 11.5396 112.7991 0.2136
1300 11.5457 112.8207 0.2135
1301 11.5517 112.8424 0.2134
1302 11.5577 112.8640 0.2133
1303 11.5638 112.8856 0.2132
1304 11.5698 112.9072 0.2131
1305 11.5759 112.9287 0.2130
1306 11.5819 112.9503 0.2129
1307 11.5879 112.9718 0.2128
1308 11.5940 112.9933 0.2128
1309 11.6000 113.0148 0.2127
1310 11.6060 113.0363 0.2126
1311 11.6121 113.0577 0.2125
1312 11.6181 113.0791 0.2124
1313 11.6241 113.1005 0.2123
1314 11.6302 113.1219 0.2122
1315 11.6362 113.1433 0.2121
1316 11.6422 113.1646 0.2120
1317 11.6482 113.1859 0.2119
1318 11.6543 113.2072 0.2118
1319 11.6603 113.2285 0.2117
1320 11.6663 113.2498 0.2116
Le Mans Master
Joined: Feb 2006
Posts: 5,762
Likes: 4
From: Chandler Arizona
7th Gear
Joined: Oct 2008
Posts: 7
Likes: 0
you need to account for Front Tire's RollOut Distance's effects
on the ET and the MPH data
i calculate in your example of
60= 1.574
330= 4.686
660= 7.344 @ 91 MPH
and
0-to-60= 3.130 ET occuring at 174 Ft distance
that the RaceCar should be accelerating approx
Ft ET MPH
-1 -.2232 0.0000
0 0.0000 6.1094 1.2477
it should have a Starting Line Rollout advantage of .2232 seconds
as a default RollOut distance of 12.0" inches or 1 Foot
the RaceCar is already traveling at 6.1094 MPH at the ZERO Ft starting line distance
another consideration to take into account
is the 660's Ft 's MPH is an "average" of 66 feet distance on the ET Slip
which is 594 Feet , and 1/2 of that 66 = 33 = 627 Feet "Mid-Point" distance
which should be pretty close in accuracy to whats going to be
printed on the ET Slip at a DragStrip.
594 6.8545 90.4494 0.3129
595 6.8621 90.4962 0.3127
596 6.8696 90.5430 0.3125
597 6.8771 90.5897 0.3122
598 6.8847 90.6364 0.3120
599 6.8922 90.6830 0.3118
600 6.8997 90.7295 0.3116
601 6.9072 90.7759 0.3114
602 6.9147 90.8223 0.3111
603 6.9222 90.8686 0.3109
604 6.9297 90.9148 0.3107
605 6.9372 90.9610 0.3105
606 6.9447 91.0071 0.3103
607 6.9522 91.0531 0.3101
608 6.9597 91.0991 0.3099
609 6.9672 91.1450 0.3096
610 6.9747 91.1908 0.3094
611 6.9821 91.2366 0.3092
612 6.9896 91.2823 0.3090
613 6.9971 91.3279 0.3088
614 7.0045 91.3734 0.3086
615 7.0120 91.4189 0.3084
616 7.0195 91.4643 0.3081
617 7.0269 91.5097 0.3079
618 7.0344 91.5550 0.3077
619 7.0418 91.6002 0.3075
620 7.0492 91.6454 0.3073
621 7.0567 91.6904 0.3071
622 7.0641 91.7355 0.3069
623 7.0716 91.7804 0.3067
624 7.0790 91.8253 0.3065
625 7.0864 91.8701 0.3062
626 7.0938 91.9149 0.3060
627 7.1012 91.9596 0.3058 .......................Mid-Point
628 7.1086 92.0042 0.3056
629 7.1161 92.0488 0.3054
630 7.1235 92.0933 0.3052
631 7.1309 92.1377 0.3050
632 7.1383 92.1821 0.3048
633 7.1457 92.2264 0.3046
634 7.1530 92.2707 0.3044
635 7.1604 92.3148 0.3042
636 7.1678 92.3589 0.3040
637 7.1752 92.4030 0.3038
638 7.1826 92.4470 0.3036
639 7.1900 92.4909 0.3033
640 7.1973 92.5348 0.3031
641 7.2047 92.5786 0.3029
642 7.2121 92.6223 0.3027
643 7.2194 92.6660 0.3025
644 7.2268 92.7096 0.3023
645 7.2341 92.7532 0.3021
646 7.2415 92.7966 0.3019
647 7.2488 92.8401 0.3017
648 7.2562 92.8834 0.3015
649 7.2635 92.9267 0.3013
650 7.2708 92.9700 0.3011
651 7.2782 93.0132 0.3009
652 7.2855 93.0563 0.3007
653 7.2928 93.0993 0.3005
654 7.3001 93.1423 0.3003
655 7.3075 93.1853 0.3001
656 7.3148 93.2281 0.2999
657 7.3221 93.2709 0.2997
658 7.3294 93.3137 0.2995
659 7.3367 93.3564 0.2993
660 7.3440 93.3990 0.2991..............-VS- 93.3990 the actual MPH @ 660 Ft
in that Picture of my Simulator
you can Input any Feet's ET,
example you can Input the 60Ft 's ET and it will calculate all the rest of
the ET's every foot for you
its possible to spot acceleration problems doing that method
you can input 60 FT , then only 330ft , then only 660 FT and see how well they
correlate like in this example
inputting only the 60FT's ET
60= 1.5740 40.9081
330= 4.6767 74.6125
660= 7.3382 91.8673
1000= 9.6648 105.3793
1320= 11.6570 112.6162
then only inputting the 330 Ft's ET
60= 1.5775 40.8289
330= 4.6860 74.4716
660= 7.3528 91.6852
1000= 9.6840 105.1671
1320= 11.6803 112.3810
then only the 660 Ft's ET
60= 1.5754 40.8749
330= 4.6805 74.5563
660= 7.3440 91.7962
1000= 9.6725 105.2940
1320= 11.6663 112.5265
then all 3-> 60,330,660 together
60= 1.5754 40.7833
330= 4.6860 74.5380
660= 7.3440 91.9242
1000= 9.6725 105.2940
1320= 11.6663 112.5265
on the ET and the MPH data
i calculate in your example of
60= 1.574
330= 4.686
660= 7.344 @ 91 MPH
and
0-to-60= 3.130 ET occuring at 174 Ft distance
that the RaceCar should be accelerating approx
Ft ET MPH
-1 -.2232 0.0000
0 0.0000 6.1094 1.2477
it should have a Starting Line Rollout advantage of .2232 seconds
as a default RollOut distance of 12.0" inches or 1 Foot
the RaceCar is already traveling at 6.1094 MPH at the ZERO Ft starting line distance
another consideration to take into account
is the 660's Ft 's MPH is an "average" of 66 feet distance on the ET Slip
which is 594 Feet , and 1/2 of that 66 = 33 = 627 Feet "Mid-Point" distance
which should be pretty close in accuracy to whats going to be
printed on the ET Slip at a DragStrip.
594 6.8545 90.4494 0.3129
595 6.8621 90.4962 0.3127
596 6.8696 90.5430 0.3125
597 6.8771 90.5897 0.3122
598 6.8847 90.6364 0.3120
599 6.8922 90.6830 0.3118
600 6.8997 90.7295 0.3116
601 6.9072 90.7759 0.3114
602 6.9147 90.8223 0.3111
603 6.9222 90.8686 0.3109
604 6.9297 90.9148 0.3107
605 6.9372 90.9610 0.3105
606 6.9447 91.0071 0.3103
607 6.9522 91.0531 0.3101
608 6.9597 91.0991 0.3099
609 6.9672 91.1450 0.3096
610 6.9747 91.1908 0.3094
611 6.9821 91.2366 0.3092
612 6.9896 91.2823 0.3090
613 6.9971 91.3279 0.3088
614 7.0045 91.3734 0.3086
615 7.0120 91.4189 0.3084
616 7.0195 91.4643 0.3081
617 7.0269 91.5097 0.3079
618 7.0344 91.5550 0.3077
619 7.0418 91.6002 0.3075
620 7.0492 91.6454 0.3073
621 7.0567 91.6904 0.3071
622 7.0641 91.7355 0.3069
623 7.0716 91.7804 0.3067
624 7.0790 91.8253 0.3065
625 7.0864 91.8701 0.3062
626 7.0938 91.9149 0.3060
627 7.1012 91.9596 0.3058 .......................Mid-Point
628 7.1086 92.0042 0.3056
629 7.1161 92.0488 0.3054
630 7.1235 92.0933 0.3052
631 7.1309 92.1377 0.3050
632 7.1383 92.1821 0.3048
633 7.1457 92.2264 0.3046
634 7.1530 92.2707 0.3044
635 7.1604 92.3148 0.3042
636 7.1678 92.3589 0.3040
637 7.1752 92.4030 0.3038
638 7.1826 92.4470 0.3036
639 7.1900 92.4909 0.3033
640 7.1973 92.5348 0.3031
641 7.2047 92.5786 0.3029
642 7.2121 92.6223 0.3027
643 7.2194 92.6660 0.3025
644 7.2268 92.7096 0.3023
645 7.2341 92.7532 0.3021
646 7.2415 92.7966 0.3019
647 7.2488 92.8401 0.3017
648 7.2562 92.8834 0.3015
649 7.2635 92.9267 0.3013
650 7.2708 92.9700 0.3011
651 7.2782 93.0132 0.3009
652 7.2855 93.0563 0.3007
653 7.2928 93.0993 0.3005
654 7.3001 93.1423 0.3003
655 7.3075 93.1853 0.3001
656 7.3148 93.2281 0.2999
657 7.3221 93.2709 0.2997
658 7.3294 93.3137 0.2995
659 7.3367 93.3564 0.2993
660 7.3440 93.3990 0.2991..............-VS- 93.3990 the actual MPH @ 660 Ft
in that Picture of my Simulator
you can Input any Feet's ET,
example you can Input the 60Ft 's ET and it will calculate all the rest of
the ET's every foot for you
its possible to spot acceleration problems doing that method
you can input 60 FT , then only 330ft , then only 660 FT and see how well they
correlate like in this example
inputting only the 60FT's ET
60= 1.5740 40.9081
330= 4.6767 74.6125
660= 7.3382 91.8673
1000= 9.6648 105.3793
1320= 11.6570 112.6162
then only inputting the 330 Ft's ET
60= 1.5775 40.8289
330= 4.6860 74.4716
660= 7.3528 91.6852
1000= 9.6840 105.1671
1320= 11.6803 112.3810
then only the 660 Ft's ET
60= 1.5754 40.8749
330= 4.6805 74.5563
660= 7.3440 91.7962
1000= 9.6725 105.2940
1320= 11.6663 112.5265
then all 3-> 60,330,660 together
60= 1.5754 40.7833
330= 4.6860 74.5380
660= 7.3440 91.9242
1000= 9.6725 105.2940
1320= 11.6663 112.5265
Last edited by MaxRaceSoftware; Oct 15, 2008 at 02:24 AM.
7th Gear
Joined: Oct 2008
Posts: 7
Likes: 0
then only inputting the 330 Ft's ET
60= 1.5775 40.8289
330= 4.6860 74.4716
660= 7.3528 91.6852
1000= 9.6840 105.1671
1320= 11.6803 112.3810
the 330 Feet's acceleration is a little weak
in that if it would continue,
it would run slower at 11.6803 @ 1/4 Mile
i don't know what Transmission was used in that Run
it also an indication that there's gear shifting Time included
from multiple gear shifts by the time the RaceCar is at 330 Feet
...and after 330 ft , by 660 FT the Cars back on course to a faster run
@ approx 11.6570 to 11.6663 range ?
60= 1.5775 40.8289
330= 4.6860 74.4716
660= 7.3528 91.6852
1000= 9.6840 105.1671
1320= 11.6803 112.3810
the 330 Feet's acceleration is a little weak
in that if it would continue,
it would run slower at 11.6803 @ 1/4 Mile
i don't know what Transmission was used in that Run
it also an indication that there's gear shifting Time included
from multiple gear shifts by the time the RaceCar is at 330 Feet
...and after 330 ft , by 660 FT the Cars back on course to a faster run
@ approx 11.6570 to 11.6663 range ?
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7th Gear
Joined: Oct 2008
Posts: 7
Likes: 0
MTVette, you could keep on developing your Excel WorkSheet further
in maybe these next directions.... that's what i'm working on in the next few Months.
With accurate Simulation of ET Times per Feet distances,
you can calculate instantaneous MPH then GForces,
then from GForces you can backtrack thru equations
to calculate HP and TQ Curves from additional Inputs in Programs
like Gears Ratios, Tire Sizes, Converter or Clutch, ETC.
or
you can use Power = Force * Velocity
or
HP = Force * Velocity
and don't need to know anything about Gear Ratios, or Tires, or ETC...
Here's ScreenShot of old Application of HP = Force * Velocity example
or a more traditional method of calculating ET Times/MPHs from HP
http://www.maxracesoftware.com/etavbwin.htm
and Pictures of Polynomial Interpolation
Note : i inputted 3.130 seconds for X , Y or Distance then = 173.8921866 Feet
and then of Cubic Spline Simulator
...but like i mentioned, a Cubic Spline Fit will not give you accurate results
and mostly worthless to persue !
in maybe these next directions.... that's what i'm working on in the next few Months.
With accurate Simulation of ET Times per Feet distances,
you can calculate instantaneous MPH then GForces,
then from GForces you can backtrack thru equations
to calculate HP and TQ Curves from additional Inputs in Programs
like Gears Ratios, Tire Sizes, Converter or Clutch, ETC.
or
you can use Power = Force * Velocity
or
HP = Force * Velocity
and don't need to know anything about Gear Ratios, or Tires, or ETC...
Here's ScreenShot of old Application of HP = Force * Velocity example
or a more traditional method of calculating ET Times/MPHs from HP
http://www.maxracesoftware.com/etavbwin.htm
and Pictures of Polynomial Interpolation
Note : i inputted 3.130 seconds for X , Y or Distance then = 173.8921866 Feet
and then of Cubic Spline Simulator
...but like i mentioned, a Cubic Spline Fit will not give you accurate results
and mostly worthless to persue !
Last edited by MaxRaceSoftware; Oct 15, 2008 at 05:10 AM.
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
...
Velocity is the first derivative of position with respect to time. Taking the derivative of the equation above, we have:
V = 3At^2 + 2Bt + C
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
the Polynomial or the Quadratic Curve Fit
is not quite accuate enough of a "Fit"
its close.... and a great estimate, and thanks for the accel.xls File !
even a Cubic Spline Fit is not going to be accurate enough to Model
every foot distance's real acceleration rate ...
is not quite accuate enough of a "Fit"
its close.... and a great estimate, and thanks for the accel.xls File !
even a Cubic Spline Fit is not going to be accurate enough to Model
every foot distance's real acceleration rate ...
7th Gear
Joined: Oct 2008
Posts: 7
Likes: 0
Agreed. It's necessarily a simple model, but given only three inputs, I'm comfortable with the results. As you rightly point out, it does ignore roll-out, as well as momentary pauses in acceleration due to shifting, and any other effects as well. My intention was to create a more accurate model than the two-parameter Wallace Racing model.
My intention was to create a more accurate model than the two-parameter Wallace Racing model
i've seen a few Guys on the Internet tackle what you are doing,
and i'm very impressed with your Solution to the Problem !
Definetly agree your 3 Parameter Model is more accurate
than Wallace's 2-Model !
from playing around with this off and on the last 20+ years,
all the research + efforts i've done into this,
shows you need at least 5 Data Inputs to achieve enough accuracy.
Luckily DragStrip's ET Slips provide 60,330,660,1000,1320 = 5 Data
and 2 more additional Inputs of the 660Ft and 1320 Ft's MPH
greatly increases the accuracy at every feet in between
once you know the 660 + 1320 MPH's,
those give you additional Info of what the
66 Feet interval's ET Times should be,
so you can calculate from those MPH's the
594 Ft's ET and then the 1254 Feet's ET
so now you know
60
330
594
660
660 MPH
1000
1254
1320
1320 MPH
and thats enough Data to just about be dead-on accuracy
in calculating every Feet's ET - MPH - GForces
then you need to apply a few Math + Curve Fitting Tricks
in Computer Code inside Loops within Loops
and breakout the Loops at the Time(Seconds) accuracy you desire.
Example->
the 1st Loop would be a .1 Tenth of a Second
then the next "inner" Loop would be at .01 Hundredth of a second
then the 3rd inner loop would be at .001 Thousandths of a second
...so that it would be extremely fast in Processor Time,
about less than 1 second to go thru thousands and thousands
of Loops
waiting for 1 Main Loop to do that job..could be a minute..whereas,
mutilple Loops within Loops ..becomes micro-seconds in Processor time
then as you probably know,
trying to Fit the Data in a Curve Fit Solution,
you can input 3 points of X,Y Data
and have all 3 correspond to exactly what you've inputted,
then fail miserably in corresponding to
4 or 5 or even more Data inputs
you can Fit 5,6, or 7 or more X,Y Data points
with Polynomial Interpolation,
but when you see that the MPH and especially the GForces
are not accurate matches to real world data .
the Et's will "appear" to look accurate enough,
but look closer at the corresponding MPH's then at the GForces,
and the Problem is more easily recognized in Modeling
TopFuel Dragster and FunnyCar's incremental Times/Mphs
...the ET Time's accuracy has to be to the .001 of a second
or better for TopFuel to model Mph + Gforces accurately enough.
Then once you've Solved all the above the next things to tackle
are the solutions to or the eliminations of,
things like Engine's RPM/SEC acceleration rate and its corresponding
Rotational Inertia Losses , as well as, all other rotating Parts
on the Vehicle.
Torque Converter Mutiplication effects or Clutch effects
By looking at the acceleration rate from around 660 Ft
to the 1320 Ft distances, this would eliminate a lot of the
Torque Converter Mutiplication effects and Clutch Slippage effects
around the 1st Gear 60ft to 330 Ft distances.
So then your 1st part of the Simulation would concentrate on
determing the Torque Curve from the around the 660ft to the 1/4 mile
....then once you establish the Torque Curve for last half of 1/4,
you would re-run the Simulation again to calculate out what would
be Torque Converter Multiplication values, LockUp Efficiencies,
Drivetrain eff, etc.
preliminary Modeling so far is very encouraging,
i think i can get the accuracy good enough
to not only correctly determine HP + TQ output
but enough resolution to see subtle effects or trends in TQ + HP
as you make Jet or Tuning changes at the DragStrip.
in other turn your RaceCar into a Rolling Dyno
with real-world results .
A poor Man's chassis Dyno or Engine Dyno
with as accurate or better results.
this HP = Force * Velocity Model is already accurate enough
to get within + or - 10 HP and 10 Torque Numbers
of Engine Dyno...using combination of 3 X,Y Inputs
but what would be need to see actual smaller changes in TQ
and HP Curves with much improved accuracy would be more like this
Le Mans Master
Joined: Oct 2007
Posts: 6,149
Likes: 11
From: Greater Detroit Metro MI, when I'm not travelling.
Not that good; a car that can spin the tires in 2nd gear will fool the system into thinking you are going 60MPH when in fact its just your tires that are doing it....
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
Le Mans Master
Joined: Feb 2006
Posts: 5,762
Likes: 4
From: Chandler Arizona
Sorry,
Glenn
Thread Starter
Race Director
Joined: Jun 2001
Posts: 10,956
Likes: 680
From: Marlboro country MA
No problem, Glenn. Everybody here already knows the equations for velocity and acceleration, but mostly for constant acceleration. This model, with a third-order polynomial for distance, invokes a varying acceleration, and hence we must use calculus to derive the velocity. Real-world track performance does exhibit variable acceleration, so we need a model which allows for this.
Last edited by MTVette; Oct 15, 2008 at 09:55 PM.