Smith & Son Ballast

[MK]

Mmmm

You’re the Math Whiz on the Team

What does 10 lbs come out to in N scale?

Lol

160 x 10 = 1600 lbs, less than a ton. 

[nickelplate759]

except that weight isn't linear.  I think  160-cubed * 10 would be closer,  which would be about 20,000 tons.

[thomasjmdavis]

160 x 10 = 1600 lbs, less than a ton. 

I am guessing you meant that in jest.....

But darn, you got me thinking about all this, and so, you are going to have to stay after class for the whole lecture....

If you applied that equation (160 x 10) to a model of a locomotive, a real loco would weigh 100 pounds, not 250 tons.
All our models are reduced in all 3 dimensions, so the volume is the volume of the prototype divided by 160cubed= V/4,096,000. Conversely, the volume of the prototype is (or should be if the model is accurate) the volume of the model multiplied by 4,096,000. And weight relates to volume (the total units of volume x weight per unit). Ballast is still a model (of ballast), so on that basis, the volume of the ballast is the cubic measure of the model ballast (how many square inches of ballast weight 10 lbs?)x 4,096,000.

A rough approximation of weight might be to multiply the weight (10 lbs) x 4,096,000.  I had thought that we might have to adjust for density (more air space in full sized ballast) but was surprised to find that sand (as a stand in for model ballast) and gravel (as a stand in for prototype ballast) have approximately the same weight- 100 lbs per cubic foot. 

So.... your 10 lbs of ballast represent about 40 million pounds, or 20,000 tons. Or 400 N scale 50 ton gondola cars.

Another way of looking at it is that, assuming the ballast you receive has a weight per cubic foot similar to sand or gravel, you will get about 172.8 cubic inches of ballast in 10 pounds, which will work out to 409,600 cu. ft (approx 15,170 cubic yards) of prototype ballast. Which sounds like a lot, but I bet there are several thousand cu.yds. of ballast in a mile of railroad track.

Based on less that precise measurements, one of my old Walthers USRA gondolas carries .6 cubic inch capacity.  So, if you squeeze, your 172.8 cu in would fit 288 gondolas (rather than 400) if filled roughly to the top, but you might exceed the scale weight limit.

Your mileage may vary based on the weight of the particular ballast used by your preferred prototype railroad.
All calculations dependent on my memory - my last math class was in 1972.

[ednadolski]

All our models are reduced in all 3 dimensions

But I thought spacetime has 11 dimensions (all that Calabi–Yau manifold stuff)?   Or we don't have to model the compactified ones?   Perhaps @GaryHinshaw can clarify?

Ed

[Maletrain]

So what do you get if you scale-up N scale WS dyed walnut shell ballast to 160:1?  (Besides the excited but confused squirrels looking for that giant walnut that must be 20' in diameter.)

[DeltaBravo]

Thank you, Like I said, I am not the math wiz. 

[nkalanaga]

Tom has the math right, and 100 lbs/cf is what the NP used for rough calculations in a crane operators manual I have. 

Also, that the sand and gravel have the same density isn't surprising, as the spaces between them also scale by the same factor.  Picture marbles and soccer balls - very different sizes, but they would still pack the same, and the open spaces would be the same shape and size, relative to the spheres.

[GaryHinshaw]

Is there an N scale PRR blend?

I don't think they have a specific blend labelled for PRR.  You should contact Dale (info above) and ask him what he would suggest.  I think Penn-Ohio would be plausible.

I hesitate to wade into the scaling discussion, but I will...  When we model, we scale the 3 macroscopic dimensions of space, and sometimes the 1 macroscopic dimension of time (with a different scale factor).  We do not scale the density of our modelling materials, so the weight of any model scales as S^3, where S is the model scale, e.g. 1/160.  Assuming N scale ballast has about the same density as prototype ballast* 10 lbs of it would correspond to 20,480 tons of prototype ballast.

* Dale told me that 10 lbs of #50 Penn-Ohio is about 1 gallon, or 0.13 cu.ft.  This gives a density of ~75 lbs/cu.ft. -- not too different from NP's rule of thumb for the prototype.

[chicken45]

I don't think they have a specific blend labelled for PRR.  You should contact Dale (info above) and ask him what he would suggest.  I think Penn-Ohio would be plausible.

I hesitate to wade into the scaling discussion, but I will...  When we model, we scale the 3 macroscopic dimensions of space, and sometimes the 1 macroscopic dimension of time (with a different scale factor).  We do not scale the density of our modelling materials, so the weight of any model scales as S^3, where S is the model scale, e.g. 1/160.  Assuming N scale ballast has about the same density as prototype ballast* 10 lbs of it would correspond to 20,480 tons of prototype ballast.

* Dale told me that 10 lbs of #50 Penn-Ohio is about 1 gallon, or 0.13 cu.ft.  This gives a density of ~75 lbs/cu.ft. -- not too different from NP's rule of thumb for the prototype.

Thanks @GaryHinshaw ! I did just that. I was asking here to see if anyone knew offhand of the different blends they offer. I also did some digging and found that a few PRR folks do indeed use the #50 Penn Ohio. Someone else said "The PRR in general used crushed granite, each stone measuring about 4".

[Point353]

So what do you get if you scale-up N scale WS dyed walnut shell ballast to 160:1?

Two photos comparing WS "fine" with S&S #50:

[nkalanaga]

Gary:  I also don't know what kind of "sand" the NP was weighing.  For ballast, they used basalt in Washington, quartzite from a quarry near Missoula in much of Montana, and who-knows-what in North Dakota and Minnesota.  They all probably had different densities, and I know basalt is denser than most rocks.  For a crane operator's manual, I'd suspect they chose basalt, for safety.  It would underestimate the weight of other materials, so the crane would be overloaded. 

If that's the case, limestone would probably be about 75 lbs/cf, as it's noticeably lighter than basalt.

[chicken45]

Two photos comparing WS "fine" with S&S #50:

Thank you for this! I'm ordering some PennOhio!

[Scottl]

Interesting comparison.  I always dry brush my ballast as a final finish, so it is easy to tint it to a precise look.

Nice ballasting job, Gary, BTW!

[bman]

I've a feeling sales of the Smith & Sons ballast are about to go up.  I'm sold.

[Lemosteam]

Anybody willing to do a similar comparo between S&S ballast vs ARM?  Wonder if it's similar.

@chicken45 , IMHO the ARM is closer to the newer/cleaned mainline ballast in this image than Gary's.