There is a relationship between Power and Tractive Effort.
Tractive effort is simply the amount of force that a locomotive can pull on the train. If you put a tension meter between a train and the loco when it’s tractive effort is 50,000 lbs, then the it will read 50,000 lbs.
Power is a force pulled over a distance. 1 HP is 33,000 ft-lbs per minute. Multiply the tractive effort over the distance pulled in a minute and you get ft-lbs:
All of the following are 1 HP
1 pound over 33,000 feet in 1 minute
10 pounds over 3,300 feet in 1 minute
100 pounds over 330 feet in 1 minute
1000 pounds over 33 feet in 1 minute
Say a 100,000 lb tractive effort loco with 6,000 HP takes off at full effort.
6,000 * 33,000 = 198 million ft-lbs. per minute.
Now divide the 100,000 lbs of tractive effort.
That leaves 1,980 feet per minute max speed at full tractive effort.
Convert to MPH and you get 22.5. This is the critical point where tractive effort and HP are both at their peaks. Trying to get too much HP at a slow speed and the wheels slip. There is no way to get any more tractive effort than HP will allow.
The locomotive will then pull 100,000 ft-lbs from 0 to 22.5 MPH then the tractive effort will decay as speed increases.
The formula for finding tractive effort at speeds greater than the critical point. At speeds less than the critical point, the wheels would slip.
(HP* 33,000)/((Speed in MPH)* 88ft/min per MPH )= Tractive Effort. Plug in the HP in question and the speed at which the tractive effort is desired.
(600033,000)/(22.588) = 100,000 lbs of tractive effort
This thoerietical loco would have this much tractive effort at these speeds.
0MPH = 100,000 lbs
10MPH = 100,000 lbs
20MPH = 100,000 lbs
30MPH = 75,000 lbs
40MPH = 56,250 lbs
50MPH = 45,000 lbs
60MPH = 37,500 lbs
70MPH = 32,143 lbs
80MPH = 28,125 lbs
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