a mathematical puzzle for the new year

[jma1009]

Stepney's side tanks will hold 81 cubic inches of water in total.

there are 2 injectors of delivery output 12 fluid ounces per minute.

if one injector is left on working and feeding, how quickly will both tanks need refilling from full up?

(no prizes, and i dont know the answer as my maths isnt that good!)

(i think for the purposes of the above, best to assume the water supply to the injector is the same as the delivery output, ignoring the amount of steam used that contributes to the output)

cheers,
julian

[mbrown]

My maths is no better than yours Julian - but my confident answer is "not long enough" and that, for a decent length of run between water stops, you would benefit from an auxiliary supply in, say, a modified LBSCR wagon. And, of course, every time you put the injector on you are likely to lose a little water, so the absolutely correct answer is probably "not nearly long enough....."

Malcolm

[andyhigham]

This is where the imperial system is really poor, various unconnected measurement units.
I would convert the injector flow to millilitres (ml). Then the the tank volume to litres and multiply by 1000 to convert to ml. Divide the tank volume by the injector volume to give minutes

[balljoint]

Using this conversion 1 cubic inch of water (in3 - cu in) = 0.58 U.K. fluid ounces of water (fl-oz Imp.), it looks like about 11.5 minutes
but I might be wrong

Colin

[andyhigham]

I make it 1.95 minutes

[flyingfox]

Greetings,
I make the capacity of the tanks 2.33 pints, which means that at 3/5 ths of a pint per minute, the tanks will last about 3 mins 50 seconds.

regards
Brian
Flying Fox

[Roger]

Yep, this is why Imperial units suck. I'll let those more familiar with them see if they can agree on a figure. That's three different ones already!

[keith1500]

Given steady conditions it would be 4 mins

[keith1500]

81 cubic inches = 1.33 litres
12 fluid oz = .0. 34 litres per minute

1.33/0.34= 3.911 minutes

[Midland]

Quite simple really 81 cu in is 46.75 fluid oz so the answer is 7 minutes and 8 seconds, that is of course, if you are not stationary. Of course if you are stationery you will not have the injector on so the answer is now, forever except that water evaporates so if the filler is open is will last a shorter time to when it is shut. Now my son did physics (yes the difficult kind) and he told me that as things approach the speed of light they get smaller so Julian it all depends on how fast you are going to go. That is of course the Imperial system. God knows what happens in metric, you will need to read the dials, check you angle of advance and pray!!! And then the US oz is a different size!!
Cheers David

Yes I know a bit facetious but couldn’t resist.

PS I cheated www.metric-conversions.org/volume/cubic-inches-to-uk-ounces-table.htm

[Midland]

Jan 4, 2016 17:11:23 GMT keith1500 said:

Given steady conditions it would be 4 mins

Only 1 injector running!!!

[Roger]

Jan 4, 2016 17:24:31 GMT Midland said:

Quite simple really 81 cu in is 46.75 fluid oz so the answer is 7 minutes and 8 seconds, that is of course, if you are not stationary. Of course if you are stationery you will not have the injector on so the answer is now, forever except that water evaporates so if the filler is open is will last a shorter time to when it is shut. Now my son did physics (yes the difficult kind) and he told me that as things approach the speed of light they get smaller so Julian it all depends on how fast you are going to go. That is of course the Imperial system. God knows what happens in metric, you will need to read the dials, check you angle of advance and pray!!! And then the US oz is a different size!!
Cheers David

Yes I know a bit facetious but couldn’t resist.

PS I cheated www.metric-conversions.org/volume/cubic-inches-to-uk-ounces-table.htm

Love it, but of course it could also be as long as it takes to evaporate, if the injector won't pick up warm water from the side tank...
Sorry Julian, it's a serious question of course, I'll say no more!

[keith1500]

I am assuming each injector is 12 fl oz. Not a combined total of 12 fl oz. Have I mis understood the question !!

[nonort]

Considerably longer than you think. If you start from the point of view that you only replace water that has been used either by the engine or up through the safety valves. Knowing your expertise from visits to the island years ago, there won't be much wasted from the safeties. Plus you will have an excellent valve gear so the engine won't waste much either. Clever people can calculate all they want, but it will also be to a certain extent effected by how heavy handed you are with the regulator and the load being propelled. My worn out Simplex will do six miles on one filling of the tanks, it has larger bores than Stepney and a much less gentle driver pulling a load of eight passengers on two trolleys. Do not panic 'Captain Mannering' if all else fails build the wagon into a tender as used by the late Keith Gammage of the Southampton Society.

[gwr14xx]

0 seconds if you are 'refilling from full up'!

[jma1009]

hi keith, yes one 12 oz per min injector running.

the purpose of the puzzle is to see how long the tanks would be emptied if one injector was left on continiuously. i thought that working out a steaming rate and combustion rate over time would be far too complicated and fraught with too many errors. i reckon one of the injectors will be on 25% of the time.

my 5"g LBSCR wagon is nearly finished to go behind for extra coal and water, but it would be nice to know how long the tanks would last to see how far or how many times i would get around an average club track circuit without the wagon and without having to stop for water.

(George Ray had already supplied the answer for his track with the Boxhill as originally designed by martin evans)

cheers,
julian

[keith1500]

I suspect in reality if you left one injector on you would overwealm the boiler, end up with less than 40 psi and still have some water left!

i run on one injector fed from the driving truck tank. The tank holds the same amount of water as the loco tanks which is coincidental but I think allows for reasonable operation ie water stops as required if using the loco tanks. However, at least the water temperature is guaranteed to operate the injector and the other advantage is a little additional traction weight provided by the loco tanks being full, albeit in your case 1.3kg. Every little helps as they say.

[jma1009]

hi keith,

assuming the injector was on say 25% of the time the object of the exercise was to see how long (in distance or time) the loco would run on it's own before a water stop. your very clever figures indicate approx 8-9 minutes in time.

oh dear, that assumes a 'speed' figure, and i am afraid i do have a tendency to even out the curves and race a bit up the banks!

cheers,
julian

[jma1009]

i would just like to thank all those who took the time and trouble to contribute to the above.

cheers,
julian

[wiltsrob]

3.91 mins assuming your boiler can support that without running out of steam pressure/space

lol.. after the horse has bolted.. should have read all the above posts before posting ..