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Calculating brake force

Started by jamespetts, September 24, 2011, 03:00:00 PM

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jamespetts

Bernd Gabriel is kindly working on code to allow for braking distances to be computed according to correct physics. This will involve allowing vehicle brake forces to be set manually in .dat files. However, I am having some trouble finding appropriate brake forces for anything other than diesel locomotives. I understand that the figure is related to weight, but I have found inconsistent information on exactly what the relationship is to the weight. Some sources suggest that the force in Kn should be approximately equal to the weight in tonnes, or perhaps slightly less; others suggest that the brake force should be very considerably less; others still, by implication, suggest that the maximum brake force in Kn should be several times greater than the weight in tonnes. Does anyone have any idea as to the correct position?
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ӔO

#1
well, simply defined, F=ma and/or F=μmg
where:
F= force
m= mass
a= acceleration
μ= coefficient of friction
g= gravity (9.81m/s/s)

http://www.bsharp.org/physics/skidmarks
http://www.csgnetwork.com/stopdistcalc.html

http://answers.yahoo.com/question/index?qid=20080422155406AAiYYPq

but these equations don't account for air drag friction or going down or up a hill.
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TurfIt

North American POV: Freight Car Braking Ratios
Locomotives and disc brake equipped passenger stock vastly different.

jamespetts

AEO,

ahh, that's not quite what I was after - perhaps I was unclear: Bernd is implementing the physics calculations (including accounting for friction and drag), but those calculations require a maximum brake force as an input value, which needs to be able to be set in the .dat file or calculated from a figure set in the .dat file. I need to know what figures to give what vehicles.
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ӔO

@james

It's possible to calculate the approximate numbers with those equations.
according to here: http://en.wikipedia.org/wiki/Rail_adhesion the friction of rail is about 0.35.
there's also here: http://en.wikipedia.org/wiki/Railway_brake which gives some experimental results on braking distances.
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jamespetts

AEO,

thank you for those. I am not sure how the rail friction itself affects the maximum brake force itself, as the brake force is one parameter and the friction another of the physics equation, and it is the brake force that I am trying to find. The second page I have seen and looked at carefully; indeed, I have gone so far as to edit the table of braking distances, as I have a copy of the book that was used as the source for that table, and the book contained additional information on the train weights, which I added to the table this afternoon. That gives a useful means of checking whether the numbers are right, but it does not tell me what the numbers should be (and, particularly, the apportionment between locomotive, carriage and wagon brake forces).
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Carl

Is the braking force feature now available for testing since the merging of the braking-physics branch and the upload of a new makeobj-experimental? If not, then apologies for being so nosey on github :) But if so, what's the new brake force parameter for the vehicle .dat files, and what is the default value for legacy paksets?

jamespetts

Brake force parameter not yet set up - working on it!
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Erik

#9
The maths are simple.

On a flat area.
Max brake force (wheels just or just not slipping.):
F=m*g*μ
Where μ is the friction between the wheels and the rails.

Inertia:
F=m*a

Together the force balance will be:
m*g*μ=m*a

Mass will cancel out.
So we get:
g*μ=a.

To get the acceleration from the speed (v [m/s]) and distance (x [m]).
a=v^2 / x

So all together we can calculate the distance it will take to stop the train.
g*μ=v^2 / x  -->  x=v^2 / (g*μ)


For slopes would it be slightly different.
the whole force balance will be:
cos(α)*g*μ=a±sin(α)*g

To calculate the brake distance:
Hill up:
cos(α)*g*μ=v^2 / x -sin(α)*g -->  x= v^2 / (( cos(α)*μ+sin(α) )*g)

Hill down:
cos(α)*g*μ=v^2 / x +sin(α)*g -->  x= v^2 / (( cos(α)*μ-sin(α) )*g)


Some trains can't brake hard enough to get the point where the wheels are just or not slipping.
You can say the bake factor of trains is how much percent of the maximum brake force they can get.