How to calculate the tractive effort of a train?

[Tim Leijten]

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

 

[BvU]

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

 

[Tim Leijten]

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:

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.

 

[Tim Leijten]

Can some one help me? ^

 

[BvU]

I don't see the 300 km/h popping up anywhere ?

Is the 6400 kW the power consumed or the power delivered ?

 

[Tim Leijten]

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).

 

[willem2]

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 coefficient 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.

 

[Tim Leijten]

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 coefficient 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 ;)

 

[willem2]

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.

 

[Tim Leijten]

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!

 

[mfb]

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.

 

[Tim Leijten]

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:

https://imgur.com/a/Ccfd1
Is it accelerating normally?

 

[BvU]

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.

 

[Tim Leijten]

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