Hi Ian,
I can't remember if this has been said, probably has, to measure the distance of the curve multiply by Pi, 3.142 if memory serves me right. 8' diameter curve is 8x3.142=25.136' distance.
Cheers,
Kim
Everyone i think robert, but on a curve you must use a soft one to go around the bends,.
Doing a measurement of gradient on an "S" bend is also hard to do.
Ian
Puckdropper mate, i am confused are you taliking to yourself or are you arguing with yourself or even agreeing with what has been said previously?
Rgds Ian
Model Railroad scales aren't mutually exclusive, you know... I've got HO, N, G (In that order because it can be pronounced.)
Anyway, about the grade math and stuff. If you want to (cold rainy day?) check your method against the actual math, you can figure out how far off you are.
There is another way to do grade measurements, one that doesn't require a calculator... just a level and tape measure. Place the level on the point you want to measure to, level it, and drop the tape from the other end of the level (making a right angle) and note the distance from the level and the distance to the ground from the tape measure.
(Sure, Puckdropper expects us to go through Geometry and Trigonometry to calculate the degree on the railroad and NOW he tells us an easier way. -- If I had thought of it earlier, I would have told you earlier.)
NeO6874 wrote: soon as I get a real income and a house I'll probably have a garden RR... and then I'll just need a supplier of coal (seeing as REAL trains ran on coal.. diesel just isn't my cup of tea)..
soon as I get a real income and a house I'll probably have a garden RR... and then I'll just need a supplier of coal (seeing as REAL trains ran on coal.. diesel just isn't my cup of tea)..
Here's something to get you started (or at least whet your appetite):
Gauge 1 Coal-Fired Live Steam
tangerine-jack wrote: NeO6874 wrote: kimbrit wrote: Oh Dan, never give up, enjoy the forum for what it is and have some fun. Gradient angles in the garden really don't matter - except in Australia!! I'm 55 years young, have trains in the garden, drink good beer 'til it flows out of my ears, enjoy spirited conversation with my mates, watch as much football as I can, but most of all, I always have fun. I do not doubt your maths, I think you are at college and do them all of the time, just let us old guys have our bit of fun, well this one anyway.Truly have a festive cheers,Kim perhaps I should stick in the MRR forums for a bit then... or hang around here more to figure out how well G scale can take grades.... HO wouldn't do so great*... and curves make it worse... i think to the effect of .5% for "broad" curves. *from both experience and what I've read - they lose ~50% pulling capacity for each % of grade or so. Dunno if this holds true with G (or if it really even matters because trains aren't 50-something cars long) Yes, please hang around here. I feel you have not only a lot to learn, but a lot to give as well. WELCOME TO THE REAL WORLD OF MODEL RAILROADING!!!!!!! Quick primer, HO trains are toys and are not real models. Real trains run outside in the dirt, so do we. Real trains get rained on, so do we. There are no critical measurments, no critical scale (unless that is what you want to do), and some garden trains do pull 50-200 cars up and down grades with no problems, in the snow.Trust me, once you taste Garden Scale, there is never going back to puny little gurlie man toy HO scale. Buy a shovel, you'll be needing it.
NeO6874 wrote: kimbrit wrote: Oh Dan, never give up, enjoy the forum for what it is and have some fun. Gradient angles in the garden really don't matter - except in Australia!! I'm 55 years young, have trains in the garden, drink good beer 'til it flows out of my ears, enjoy spirited conversation with my mates, watch as much football as I can, but most of all, I always have fun. I do not doubt your maths, I think you are at college and do them all of the time, just let us old guys have our bit of fun, well this one anyway.Truly have a festive cheers,Kim perhaps I should stick in the MRR forums for a bit then... or hang around here more to figure out how well G scale can take grades.... HO wouldn't do so great*... and curves make it worse... i think to the effect of .5% for "broad" curves. *from both experience and what I've read - they lose ~50% pulling capacity for each % of grade or so. Dunno if this holds true with G (or if it really even matters because trains aren't 50-something cars long)
kimbrit wrote: Oh Dan, never give up, enjoy the forum for what it is and have some fun. Gradient angles in the garden really don't matter - except in Australia!! I'm 55 years young, have trains in the garden, drink good beer 'til it flows out of my ears, enjoy spirited conversation with my mates, watch as much football as I can, but most of all, I always have fun. I do not doubt your maths, I think you are at college and do them all of the time, just let us old guys have our bit of fun, well this one anyway.Truly have a festive cheers,Kim
Oh Dan, never give up, enjoy the forum for what it is and have some fun. Gradient angles in the garden really don't matter - except in Australia!! I'm 55 years young, have trains in the garden, drink good beer 'til it flows out of my ears, enjoy spirited conversation with my mates, watch as much football as I can, but most of all, I always have fun. I do not doubt your maths, I think you are at college and do them all of the time, just let us old guys have our bit of fun, well this one anyway.
Truly have a festive cheers,
perhaps I should stick in the MRR forums for a bit then... or hang around here more to figure out how well G scale can take grades.... HO wouldn't do so great*... and curves make it worse... i think to the effect of .5% for "broad" curves.
*from both experience and what I've read - they lose ~50% pulling capacity for each % of grade or so. Dunno if this holds true with G (or if it really even matters because trains aren't 50-something cars long)
Yes, please hang around here. I feel you have not only a lot to learn, but a lot to give as well. WELCOME TO THE REAL WORLD OF MODEL RAILROADING!!!!!!! Quick primer, HO trains are toys and are not real models. Real trains run outside in the dirt, so do we. Real trains get rained on, so do we. There are no critical measurments, no critical scale (unless that is what you want to do), and some garden trains do pull 50-200 cars up and down grades with no problems, in the snow.
Trust me, once you taste Garden Scale, there is never going back to puny little gurlie man toy HO scale. Buy a shovel, you'll be needing it.
well, now that we've covered those bases - HO is a necessity at the moment (college kid).
-Dan
Builder of Bowser steam! Railimages Site
Jack once more i agree with you but i must take you aside and have a man to man talk to you; what time is it there; i know what time it is here and you are up to late or up to early. Its nearly 1 pm here wed 13 th and i think you are 14 hours behind us, so add 10 hours and it is 10 pm last night, right?
IaPS i am knocking off for lunch now,
That brings up a very good point, Tom. There are a million and one ways to do whatever it is that needs to be done in the garden. No one way is right or wrong. Whatever works for you is the right way.
Guys like Dan are probably getting a culture shock on this forum. I've found that it works like this:
Nobody is under any obligation to pay the least bit of attention to what anybody else has to say, take what you can use and leave the rest. I've learned a lot, adapted some ideas and moved in directions I would never have thought of myself. This is in fact MUCH different than the HO forum. I like it this way. I spent many years being stressed over a job that requires 100% accuracy as the only acceptable standard, now I want to be a bit more casual. Maybe it's good, maybe bad, I don't know, but I like the format the way it is.
The Dixie D Short Line "Lux Lucet In Tenebris Nihil Igitur Mors Est Ad Nos 2001"
Tom mate, i read your post several times and i like it but i can't quite see what you are getting out of what you did. I am even astute enough to work out that you did not use a metric measure at all but 40" and every 10' and a quarter of a cm is not actually that is it? its 1/10"
Jack once more we are in agreement.
Rgds ian
Tom Trigg
To all my good mates that want to divide anything by nought i say phooey. This is digging in the dirt in your backyard mate, and when it is over 30 deg C a cool beer is more important.
I really think i am pretty right, i am convinced that over 1 m track and this metres position and shape changes every time i move on to another small section (276 mm) of track; if i drop 2 cm i have a 2% gradient and i also have about a 2.2deg gradient. Over 4m i have in fact dropped 8 cm, i have proved that now ith my water level.
If anyone disagrees tell me what you think; or any test i can do to get a more realistic figure.
rgds ian
kimbrit wrote:Oh Dan, never give up, enjoy the forum for what it is and have some fun. Gradient angles in the garden really don't matter - except in Australia!! I'm 55 years young, have trains in the garden, drink good beer 'til it flows out of my ears, enjoy spirited conversation with my mates, watch as much football as I can, but most of all, I always have fun. I do not doubt your maths, I think you are at college and do them all of the time, just let us old guys have our bit of fun, well this one anyway.Truly have a festive cheers,Kim
All well and good; HOWEVER, the question here is that if you have a spirit level equipped with an adjustable vial and you set that vial to give 1 degree of rise, how do you calculate the resulting percentage of grade that the given 1 degree of rise will give.
As far as the curveature is concerned it would appear that a length measurement along the centerline of the track gauge is the consensus for distance.
I firmly agree with Kim on that point, Dan. Don't get discouraged because of a little debate, it's only a forum and what's more we are arguing about TOY trains for Pete's Sake!
Your math is on the mark, there are no errors in your position, it's just that it really, truly doesn't matter in the garden if the grade is + or - a few points just as long as it looks good and the engines can handle them. On my Dixie D SL I did a quick calculation on a scrap paper for what I wanted the maximum grade to be, then went outside with a 2x4 and a tape measure and made it so.
Have fun!!!
kimbrit wrote:This is the model world Dan and in my garden I certainly will not be using the maths I've been shown how to use, nor stand in a corner with the pointy hat on because I do it another way, rightly or wrongly. The truth of the matter is I never work out a % grade or a degree of grade because in my garden it doesn't matter, I work out a smooth gradient - as said. I will always maintain though that a gradient must be between 0 and 90 degrees, I know because I've walked up them in my hiking days. In my climbing days I've also climbed reverse gradients - when 90 degrees is passed and it overhangs. I am now at home with a beer and I am going to incline myself in my favourite chair and grade tonights TV with points out of 10. I will be dividing nothing by zero because that is a pointless exercise, except perhaps when Gail serves me my fish, chips and mushy peas and as I eat it, degree by degree, I will appreciate that said meal is diminishing, bit by bit, towards zero and in the end I will not be able to divide it anymore. Such is life, by the way I'm not a her and show us some pics of your railway.Festive cheers,KimPS whatever T-Jack was on about, I probably agree.
This is the model world Dan and in my garden I certainly will not be using the maths I've been shown how to use, nor stand in a corner with the pointy hat on because I do it another way, rightly or wrongly. The truth of the matter is I never work out a % grade or a degree of grade because in my garden it doesn't matter, I work out a smooth gradient - as said. I will always maintain though that a gradient must be between 0 and 90 degrees, I know because I've walked up them in my hiking days. In my climbing days I've also climbed reverse gradients - when 90 degrees is passed and it overhangs. I am now at home with a beer and I am going to incline myself in my favourite chair and grade tonights TV with points out of 10. I will be dividing nothing by zero because that is a pointless exercise, except perhaps when Gail serves me my fish, chips and mushy peas and as I eat it, degree by degree, I will appreciate that said meal is diminishing, bit by bit, towards zero and in the end I will not be able to divide it anymore. Such is life, by the way I'm not a her and show us some pics of your railway.
Festive cheers,
PS whatever T-Jack was on about, I probably agree.
I give up... ifyou fail to see why I stated you are wrong in your method of determining gradient, then there is no point for going on further. I never said one way was "more right" than the other for modeling, but that your method will provide a gradient that is (roughly) 50% steeper than what was intended - as well as you are not actually measuring the gradient of a given line/angle (amount of rise for a given run), but what part/percentage of 90 degrees that a given line/angle is.
In my post, I had hoped that I could offer better examples of gradient, but it apperas that my originally well intended posts have degraded into some form of childish argument over relatively simple mathematics which may, or may not be being misconstrued by one or both of us.
with that, I wish the best of luck to everyone in their respective endeavors.
The question is, how to measure the gradient of a curve.
The answer is pretty straightforward. I assume you already know how to measure the gradient of straight track based on calculating rise / run, using your stepping block and level. So go ahead and calculate the rise by that method, from the beginning of the spot on the curve you want to measure to the end.
Now, divide that number by the total distance around the curve. You can calculate this in one of two ways (as well as a number of more complicated ways):
1. If you're using preformed curved track sections of a known radius: multiply the radius by 6.3 (2pi) to get the diameter of the circle. Divide by the number of segments needed to make a circle (usually 12 or 16). That's the length of each curved track segment. For example, 10' diameter (5' radius) track has a diameter of approximately 31.5. Aristo-Craft 5' radius track comes 12 segments to a circle. Therefore each segment is approximately 31.5 inches (31.5 feet / 12 = 31.5 inches) long.
2. If not, get a piece of string. Fasten one side to a sleeper where you want to start measuring, and stretch it along the curved side of one of the rails until you reach the end. Mark the end, stretch the string out straight and measure it. (You can also do something similar with a soft measuring tape instead if you prefer). If that's still not precise enough for you, measure each rail and take an average between them to get the distance measured down the center of the track.
You now have the vertical distance and the horizontal distance. Divide one by the other and you have your gradient.
tangerine-jack wrote:Theoretical mathematics has no application in the garden railroad. Since nobody here will even attempt a 90 degree slope or greater than 50% gradient, then nobody will even approach the idea of a complex infinity so division by zero is a red herring to the argument as our defined limits are from 0 gradient to a maximum useable of maybe 6 or 8%.
Theoretical mathematics has no application in the garden railroad. Since nobody here will even attempt a 90 degree slope or greater than 50% gradient, then nobody will even approach the idea of a complex infinity so division by zero is a red herring to the argument as our defined limits are from 0 gradient to a maximum useable of maybe 6 or 8%.
That was the point I am trying to make...sort of...
I was (maybe poorly) trying to show that kimbrit's method has a large margin of error (50% give or take) to figure out the actual grade of an incline; as well as the error in her information regarding that a grade of 100% is 90º (to it's "flat" plane of reference).
Ok alrighty then, let's boogie.
True Ne06847, but that all depends on what zero is. There are contexts in which division by zero can be considered as defined. For example, division by zero in the extended complex plane is defined to be a quantity known as complex infinity. However zero does not have a multiplicative inverse under any circumstances. Limits involving division by a real quantity which approaches zero may in fact be well defined depending on application of the defined limits of the mathematical argument.
To sum up:
Sticks are free, string cost a dollar, a yard (meter) stick two dollars, and a day in the garden laying track is priceless.
kimbrit wrote:I have to say that I disagree with this, you can not divide by 0. 90 degrees divided by 0 is 0
I have to say that I disagree with this, you can not divide by 0. 90 degrees divided by 0 is 0
actually anything divided by 0 is unsolvable (without the use of some really involved math). What I have been trying to point out to you is that your method gives what percent of 90 DEGREES an angle is (part/whole). it in no way, shape, or form, gives an accurate measure of the GRADIENT (rise/run).
If you were to do the math that has been previously shown, you will see that you are completely wrong.
If I was going to make a grade of 1%, the angle of the grade (as compared to the ground) would be atan(.01) which is .57 degrees. If I was to apply YOUR method, (1% of a 90 degree angle), you would be going up(or down) a grade of 1.5%, which is tan(.9). Now, for small gradients, this is pretty close, I'll give you that - BUT if you were to make anything steeper than that, you will quickly realize that the part of a 90 degree angle method will give you a grade of mugh higher than you would have thought. for example: 3% grade -> atan(.03) = 1.71 degrees; 3% of 90 is 2.7 degrees -> tan(2.7) = 4.7%. thats over 50% steeper than the grade you were originally trying to create.
Hello Jack,
Best regards from our techie:
Yours is the practical approach that will get quick and "close enough" results. Mounting one of the Sears modules on a flatcar will make it even easier.
Best regards
ER
Interesting topic. All the math is very fine, but only John Busby came close to answering the original question, how to measure on a curve. All you math majors should realise that this exact problem is why calculus was invented. The question is how small a slice of a circle can you cut before it is not curved anymore? Using prof. Busby's logic, the smaller straight segment of the curve you take (his expample was 100mm which is fine) the more accurate a measurment you will get. Take the segments and apply the mathematical formulas for gradient and continue on until you have completed the curve.
Practical application is very easy, use a shorter a piece of wood and take more measurments, OR use a longer piece of wood to measure from the origin of the rise to the terminus in a straight line to get the total gradient, then adjust the track down the length so it is smooth.
Without proper survey tools we have to suffice with string and water levels. But that's OK, because that is all they had to build the pyramids with and it worked just fine.
I have to say that I disagree with this, you can not divide by 0. 90 degrees divided by 0 is 0, 45 degrees divided by 0 is 0. 0 does exist in degrees in that it is the horizontal. I agree a 1 in 1 rise is 45%, I've already said this, so what is a rise of 1 in .75? or a rise of 1 in 0.5. These are gradients and will have a percentage value as well as a degree value, the percentage value being greater than 45%. I have no idea about a tan, I do not know what it is or isn't and as already stated it doesn't really matter when all you want to do is lift your line a few inches over a given run, straight or curve. My main point in all of this, not exactly the answer to the topic, was to get a gradient with an equal rise (or fall) that does not punish the loco to much.
now that's a nice incline
Gentlemen;
I must say i am proud to assciate with all of you, this is one of those rare times on this forum where we have a considerable amount of dialogue about a decent subject and you can see who is not participating. The people i am referring too will know who they are.
The maths is too much for me and i really don't care that much about degrees anyway, % is good enough. My method of using centimetres for height and metres for distance is very simple and accurate. you use a 1 metre length straightedge and have your stepping blocks in centimetres and each centimetre will be a %.
But on a curve a straight straightedge is no good because you have to go round a bend. My logic, have a straightedge that is straight vertically but bent to suit the curve horizontally. If you can; even simpler, use a soft tape and measure your 1 metre around the curve and it will not matter if your straight edge is straight horizontally as the the two ends of the measued distance have already been established and all you are establishing is the difference in height between the two and as you know the distance already the same formula will apply. length in M/ height in cM = %
I know this is not 100 % right but it will give a rough indication and in this hobby surely this will suffice. But if you have 100 points % and 90 points in a right angle, surely a % must be about 9/10 of a degree?
Rgds Ian.
PS Trigg if you read this, you will notice that the people you reagrd as experts, are conspicuous by their absence in this discussion.
Your math is based solely on the 0 to 90 degree markers, and saying that each degree is a certain percentage of 90. HOWEVER, it has nothing to do with the actual mathematical formula for determining slope(gradient).
Puckdropper has alredy shown the math. If you would apply those formulas to what you're trying to say - you will see where you are wrong. You will also see how I came up with my figures.
The 1:4, 1:8, etc. figures I put were the actual rise:run for a given angle/grade. Probably the easiest way to demonstrate this would be to take a sheet of graph paper and a protractor. You will see that an angle with 1 unit of rise for every unit of run (1:1) will have an angle of 45º. a 90º angle is unsolvable - you simply cannot divide by 0.
if you still don't believe me, here is the math.
As you can see, the tangent of a 45º angle is a 100% grade; and the tangent of a 26.5º angle makes a 50% grade (so my math was off before, but not by much - 9% roughly).
a climb of 75% (grade) is an angle of 36º
a climb of 99% (grade) is an angle of 44.7º
I would be careful of taking 45 degrees as being = to 100%, what about a climb of 75%? or 99%. A slope, or gradient, is between 0 and 90 degrees as any hiker will tell you, the top end being a climb rather than a hike. I don't know about the states but here in the UK road steepness is now given in % rather than 1 in 4, 1 in 3 etc and cars can tackle very steep slopes, hence 0-90 degrees, and 1 degree = 0.9 %. In the end it doesn't really matter, if you are building a gradient, make it gentle!
Get the Garden Railways newsletter delivered to your inbox twice a month