I How to calculate the tractive effort of a train?

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To calculate the tractive effort of a train, the formula used is Power divided by speed in meters per second, but this may yield unrealistic values if not applied correctly. The discussion highlights the importance of using consistent units and understanding the drag coefficients (A, B, C) that affect a train's performance. The ES64F4 locomotive is noted for its high power rating, which allows for speeds exceeding typical limits, but the maximum speed is often constrained by safety regulations and operational conditions. Users suggest that the drag coefficient may need adjustment for more accurate simulations, as well as considering factors like rolling resistance and train length. Overall, achieving realistic simulation results requires careful calibration of these parameters.
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Hi there again,

I am trying to correctly calculate the tractive effort pf a train, currently i do this:
Power/speedMpS = TractiveEffort
I got that from here.
But it doesn't provide realistic values, so i am wondering, what is the correct way of calculating tractive effort of a train?

Thanks
 
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Tim Leijten said:
But it doesn't provide realistic values
says who ?
Are you using consistent units ? speedMpS smells like 'perhaps not'... unless you mean speed in m/s

Energy = force x distance

Power = energy / time

speed = distance / time

With a constant force you end up with your Power = force x speed
 
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BvU said:
says who ?
Are you using consistent units ? speedMpS smells like 'perhaps not'... unless you mean speed in m/s

Energy = force x distance

Power = energy / time

speed = distance / time

With a constant force you end up with your Power = force x speed
Says i, I have compared it with train simulators, and I also added a friction curve to it which says my train should go ~300km/h when it should be 140.
I think you misunderstood me, i need to calculate tractive effort, which is in Newton(force).
I already k ow the power of the train(6400kW).
SpeedMpS is indeed speed in meter per second.

edit:
proof that i don't think it is correct, where the lines cross is the speed the train will reach on level track:
Untitled.png

X axis is in m/s and y-axis is in kN.
The first is the program I created, and the second program is fcalc, a program that calculates the friction of trains made for MSTS.
 

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Can some one help me? ^
 
I don't see the 300 km/h popping up anywhere ?

Is the 6400 kW the power consumed or the power delivered ?
 
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BvU said:
I don't see the 300 km/h popping up anywhere ?

Is the 6400 kW the power consumed or the power delivered ?
Where the lines cross in the chart(~95) is the balancing speed of the train in m/s.
Multiply by 3.6 and you get ~300(even more now i think about it)
The 6400kw is the power rating i got from wikipedia, which i believe is the power delivered(but not sure).
 
It seems you mean this locomotive?
https://en.wikipedia.org/wiki/EuroSprinter#ES_64_F
The Davis Coefficients seem to be for only the locomotive. A = 1070 seems ok, 1070 N rolling resistance with a normal force of 850kN is a drag coefficent of 0.00125. I can't seem to find any realistic values for B. C is from the drag equation with a Cd of 1.0. and a frontal area of 12.9 m^2. This drag coefficient seems a bit high for a single locomotive, but is likely 2-3 times too low for a long train. The top speed is mainly determined by the value of C.
If you double A, or B, v changes very little. (I typed 1070v + 28.6v^2 + 7.4 v^3 = 6400000 in wolfram alpha)

To get down to a maximum speed of 140 km/hr = 39 m/s you still need to take C = 100. I think the maximum speed of this train comes from safety considerations. 140 km/hr is a common maximum speed on railways in europe. The power is likely needed to accelarate fast enough when pulling a long train or pulling up an incline. According to the wikipedia article the ES64F is used for freight trains.
 
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willem2 said:
It seems you mean this locomotive?
https://en.wikipedia.org/wiki/EuroSprinter#ES_64_F
The Davis Coefficients seem to be for only the locomotive. A = 1070 seems ok, 1070 N rolling resistance with a normal force of 850kN is a drag coefficent of 0.00125. I can't seem to find any realistic values for B. C is from the drag equation with a Cd of 1.0. and a frontal area of 12.9 m^2. This drag coefficient seems a bit high for a single locomotive, but is likely 2-3 times too low for a long train. The top speed is mainly determined by the value of C.
If you double A, or B, v changes very little. (I typed 1070v + 28.6v^2 + 7.4 v^3 = 6400000 in wolfram alpha)

To get down to a maximum speed of 140 km/hr = 39 m/s you still need to take C = 100. I think the maximum speed of this train comes from safety considerations. 140 km/hr is a common maximum speed on railways in europe. The power is likely needed to accelarate fast enough when pulling a long train or pulling up an incline. According to the wikipedia article the ES64F is used for freight trains.
Hi, thanks for your reply!
You are almost right, the locomotive I am talking about is the ES64F4 or also called the BR189.(But they probably share the same specs)
The coefficients are indeed only for the locomotive, as i will calculate the drag for each locomotive seperatly.
A C of 100 does indeed result in ~39 m/s, but I still am having the idea, it is not behaving as it should as i think the resistance is rising too rapidly(tell me if i am wrong)
So could you maybe tell me what I have to do to make it correct, or why the maximum speed i calculated is more then 300km/h?
In train simulator 2017, MSTS, and youtube videos, the train doesn't seem to go faster then 140, so i seem to be doing something wrong somewhere.
From your post, you seem to be atleast trying to explain what is happening, so could you maybe tell a bit more?
A C of 100 seems wrong to me, and it also seems that fcalc has a reason for using a C of 7.4.

Could you explain a bit more?Thanks!

Edit:
I ahve to correct something, I read someone saying that the ES64F4/BR189 can indeed go faster, 230km/h according to that single person(unsure if true) But i also saw a this train:
https://nl.wikipedia.org/wiki/ÖBB_1216 Which should be able to reach 230km/h according to the site, and it has specs very close to the ES64F4/BR189, and i even saw a video where they got it to 350km/h!
So it is indeed possible, but is it realistic? And why is it not simulated in simulators? Could you maybe talk a bit more about that if you know more?
Thanks ;)
 
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Tim Leijten said:
Hi, thanks for your reply!

So could you maybe tell me what I have to do to make it correct, or why the maximum speed i calculated is more then 300km/h?
In train simulator 2017, MSTS, and youtube videos, the train doesn't seem to go faster then 140, so i seem to be doing something wrong somewhere.
From your post, you seem to be atleast trying to explain what is happening, so could you maybe tell a bit more?
A C of 100 seems wrong to me, and it also seems that fcalc has a reason for using a C of 7.4.
The value of C from fcalc comes from the equation for air drag
F_d = \frac {1}{2} C_d \rho A v^2
F_d is the drag force, C_d the drag coefficient, A is the frontal area of the train, and ρ the density of air. you used 1.0 for C_d in fcalc.
I found some more data for trains here" http://by.genie.uottawa.ca/~mcg3341/AerodynamicsOfHighSpeedTrains.pdf
On page 372:
A ranges from 0.008 m to 0.02 m where m is the train mass, this matches the values you used.
B = 10-4 m + 0.2 L where L is the train length in metres. this would match the value you used for an 87 ton locomotive and a train length of ~100m.
C = (1/2) ρ A Cd. Cd can range from 1 for highly streamlined trains, to 10~15 for freight trains. the highest value here would indeed produce a C of about 100.
A, B and C will depend very much on the train that is pulled, so we don't really know. Long freight trains can be pulled with more than one locomotive also. For a single locomotive the top speed would still be much higher than 140 km/hr. I don't think this maximum is determined by the power of the engine in that case.
 
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  • #10
willem2 said:
The value of C from fcalc comes from the equation for air drag
F_d = \frac {1}{2} C_d \rho A v^2
F_d is the drag force, C_d the drag coefficient, A is the frontal area of the train, and ρ the density of air. you used 1.0 for C_d in fcalc.
I found some more data for trains here" http://by.genie.uottawa.ca/~mcg3341/AerodynamicsOfHighSpeedTrains.pdf
On page 372:
A ranges from 0.008 m to 0.02 m where m is the train mass, this matches the values you used.
B = 10-4 m + 0.2 L where L is the train length in metres. this would match the value you used for an 87 ton locomotive and a train length of ~100m.
C = (1/2) ρ A Cd. Cd can range from 1 for highly streamlined trains, to 10~15 for freight trains. the highest value here would indeed produce a C of about 100.
A, B and C will depend very much on the train that is pulled, so we don't really know. Long freight trains can be pulled with more than one locomotive also. For a single locomotive the top speed would still be much higher than 140 km/hr. I don't think this maximum is determined by the power of the engine in that case.
Thanks!
So it is normal that this locomotive goes that fast?(without cargo, 300km/h in my graph)
Are you saying i should increase Cd a bit?(1.8?)
thanks for the explanation, it helps me understanding fcalc, but one question?
Are the results i am getting normal for this locomotive?
Maybe you have a tip on a simpler to graph locomotive that has a real max speed of 100km/h or so?
Thanks!
 
  • #11
It is normal that a cargo locomotive without cargo has much more power than it needs to travel alone, on a straight track, with zero acceleration at its design speed.
Otherwise it would break down at the first slope.
 
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  • #12
mfb said:
It is normal that a cargo locomotive without cargo has much more power than it needs to travel alone, on a straight track, with zero acceleration at its design speed.
Otherwise it would break down at the first slope.
Thanks, so it is normal a locomotive can go 300km/h without cargo if wikipedia says max is 140?
And does this means that train simulator is wrong as it goes only 145km/h without cargo?
And here an gif of it accelerating in a simulation i made:
8JO4tyQ
https://imgur.com/a/Ccfd1
Is it accelerating normally?
 
  • #13
A bit fast, more like an automobile: 10" to get to 100 km/h. I'm pretty convinced loc drivers don't put the full traction on when taking off.
 
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  • #14
BvU said:
A bit fast, more like an automobile: 10" to get to 100 km/h. I'm pretty convinced loc drivers don't put the full traction on when taking off.
They probably won't indeed ;)
But asisde from the fact that i am starting full throttle and wheelslip would probably ocur, does it seem realistic if i got glue wheels?
I probably need to go and simulate the starting friction < 3km/h as it is harder to get something moving then keeping it moving.
But would it seem realistic from e.g. 10km/h?

Thanks
 
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