THE WHITE
LIGHTNING
ELECTRIC POWERED LAND SPEED RECORD
ATTEMPT CAR
At the DWRA Web Site you will read that "Santa Ana, California, businessman Ed Dempsey formed WORLD RECORD PERFORMANCE ASSOCIATES, INC. to bring together the brightest minds and best talent to attempt a series of world record assaults." I am proud to be part of Ed's team and am looking forward to participating in more cool and totally bizarre, but doable ideas!
On this first WRPA project I didn't invent a thing. Again, see the WHITE LIGHTNING Web Site to learn how this innovative machine evolved and how it uniquely combines a host of earlier inventions into an all new invention. On this project, I am "The Performance Analyst" - meaning I use Newton's Law's of Motion along with a combination of measurements and estimates to establish the traction forces, rolling resistance forces and aerodynamic drag forces at any instant of time. This tells me how much the machine will be accelerating as it progresses along the track and in turn enables me to calculate its speed anywhere along the race course. It is all based on:
å F = ma
This is just math and engineer peoples shorthand notation to remind them that the sum (å - the Greek letter called sigma) of all the forces (F) pushing and pulling on a body equals the mass (m) of the body times its resulting acceleration (a). They call it a "formula" and that scares a lot of people away. It shouldnt - it is not a big deal! Learning Microsoft Front Page to do this Web Site - now that was a big frustrating deal. My hat is off to all the kids who can create this web stuff just using HTML!
Unfortunately in our instance, Newton's Calculus can't be used because the math is too complicated to be solved in a closed form, so it all has to be done on a computer using teeny little time steps. Here is how we do that. Every one thousandth of a second, the computer calculates all the forces, then it sums them to find the current net acceleration. Then, this amount of acceleration is used to calculate just how much speed will increase and just how much distance will be covered in the next one thousandth of a second. This is repeated 180,000 times for a 3 minute run! It really is amazing to see today's computers whip out a few million calculations in just a couple of blinks of an eye!
The real problem is to take all that numerical data and make something comprehensible out of it. A data "summary" of a typical computer run is shown here. To simplify looking at the output, we just saved the numerical data as each 10 second interval goes by and left the tons of intermediate numbers hidden.
Electric LSR Vehicle - Acceleration, Speed and Distance VS Time Calculations |
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by Douglas J. Malewicki, President/Chief Scientist, AeroVisions, Inc., February 2, 1997 |
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This numerical integration is based on: |
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1) Fixed constant Horsepower output through an infinitely variable transmission (no loss of power as batteries heat up) |
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2) No reduction in motor horsepower output with at higher altitudes (it is not an aspirated internal combustion engine using air!) |
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Vehicle ID = |
CCC 300 MPH - condition (A) |
W = Gross Weight (lbs) = |
2500 |
HP = Horsepower = |
400 |
Cd = Aerodynamic Drag Coefficient = |
0.131 |
A = Frontal Reference Area (sq. ft.) = |
4.9848 |
CL = Aerodynamic Downforce Lift Coefficient = |
0 |
P = Tire Pressure (PSI) = |
100 |
Cr = Rolling resistance coefficient = |
0.02 |
Mu = Traction Limit Coefficient = |
0.4 |
N = % Gear Train/Overall Efficiency = |
90 |
SLOPE = % Road Grade = |
0 |
Vwind = Headwind (MPH) = |
0 |
H = Elevation above Sea Level (feet) = |
4300 |
T = Air Temperature (degrees F) = |
80 |
Calculated Basic Terms: |
|
CdA = Effective Frontal Area (sq ft) = |
0.6530088 |
CLA = Effective Down Force Area (sq ft) = |
0 |
Maximum Traction Force (lbs) = |
1000 |
Pounds per Horsepower Ratio (lbs/HP) = |
6.25 |
Horsepower to Drag Ratio (HP/sq ft) = |
613 |
Air Density Ratio (from table) = |
0.85 |
FORCES |
HORSEPOWER REQUIRED |
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Time (sec) |
Distance (Miles) |
Current Speed (MPH) |
Current Distance (feet) |
F aero down force (lbs) |
F rolling (lbs) |
F aero drag (lbs) |
HP rolling |
HP aero drag |
HP NET |
F Net Traction (lbs) |
Resulting Acceleration (g's) |
Increase in Speed (DMPH) in last .1 sec |
Increase in Distance (Dfeet) in last .1 sec |
0 |
0.0 |
0 |
0 |
0 |
54 |
0 |
0 |
0 |
0 |
1000 |
0.400 |
0.88 |
0.1 |
10 |
0.1 |
88 |
644 |
0 |
60 |
11 |
14 |
3 |
343 |
1000 |
0.400 |
0.88 |
12.9 |
20 |
0.5 |
167 |
2549 |
0 |
78 |
39 |
35 |
18 |
308 |
692 |
0.277 |
0.61 |
24.5 |
30 |
1.0 |
216 |
5381 |
0 |
95 |
66 |
55 |
38 |
267 |
463 |
0.185 |
0.41 |
31.7 |
40 |
1.7 |
251 |
8821 |
0 |
109 |
90 |
73 |
60 |
227 |
339 |
0.136 |
0.30 |
36.8 |
50 |
2.4 |
277 |
12703 |
0 |
121 |
109 |
89 |
81 |
190 |
257 |
0.103 |
0.23 |
40.7 |
60 |
3.2 |
297 |
16920 |
0 |
131 |
125 |
104 |
99 |
157 |
198 |
0.079 |
0.17 |
43.6 |
70 |
4.1 |
312 |
21394 |
0 |
139 |
139 |
116 |
115 |
129 |
154 |
0.062 |
0.14 |
45.8 |
80 |
4.9 |
324 |
26068 |
0 |
146 |
149 |
126 |
129 |
104 |
121 |
0.048 |
0.11 |
47.6 |
90 |
5.9 |
334 |
30898 |
0 |
151 |
158 |
135 |
141 |
84 |
95 |
0.038 |
0.08 |
49.0 |
100 |
6.8 |
341 |
35852 |
0 |
156 |
165 |
142 |
150 |
68 |
75 |
0.030 |
0.07 |
50.1 |
110 |
7.7 |
347 |
40902 |
0 |
159 |
171 |
147 |
158 |
54 |
59 |
0.023 |
0.05 |
50.9 |
120 |
8.7 |
352 |
46028 |
0 |
162 |
176 |
152 |
165 |
43 |
46 |
0.018 |
0.04 |
51.6 |
130 |
9.7 |
355 |
51214 |
0 |
164 |
179 |
156 |
170 |
35 |
36 |
0.015 |
0.03 |
52.1 |
140 |
10.7 |
358 |
56447 |
0 |
166 |
182 |
159 |
174 |
27 |
29 |
0.012 |
0.03 |
52.5 |
150 |
11.7 |
360 |
61718 |
0 |
167 |
184 |
161 |
177 |
22 |
23 |
0.009 |
0.02 |
52.9 |
160 |
12.7 |
362 |
67018 |
0 |
169 |
186 |
163 |
180 |
17 |
18 |
0.007 |
0.02 |
53.1 |
170 |
13.7 |
364 |
72341 |
0 |
169 |
188 |
164 |
182 |
14 |
14 |
0.006 |
0.01 |
53.3 |
180 |
14.7 |
365 |
77682 |
0 |
170 |
189 |
165 |
184 |
11 |
11 |
0.004 |
0.01 |
53.5 |