Power and Economy - Calculus

[Diesel Dave]

Chaps,

I've had a little play around with some spreadsheet calculations, mostly based on personal experience and some anecdotal stories from other dieselbike riders.

On many occasions new builders ask for details of how much HP delivers how much speed and what fuel economy can be expected from certain engines. The enclosed details my experiences and expectations

Firstly dealing with HP vs Speed, please bare in mind these are 'best possible' speeds and ANY impedance such as headwinds or inclines are going to make a big difference to the results - it's intended as a starting point for gearing calculations for new builds:


MPH HP
48 7
52 8
55 9
60 10
65 11.8
70 14
75 16
80 19
85 22
90 25
100 34
115 53


Next comes the tricky question of projecting fuel economy figures - not easy but given the figures above and looking at the manufacturers data for fuel consumption (usually in the engine manual - performance charts on g/Kwh).

At 55mph the Lombardini engine in the enfield is making it's max HP of 9 and consuming 300g of fuel per KW/Hour - putting these calculations into a spreadsheet I get the results of 140mpg. this is almost exactly what I get on the road when bashing down the motorway for miles at full throttle when going to the Hamm rally. In Commuting use I get about 180-190 as half the journey is at 20mph filtering between lines of heavy traffic.

So why all this bother with calculus?

Well I'm going to post some predictions for the Tiger and then you can all keep me honest when I post the actual experiences later on.

Notes:

1) the Tiger's 1000cc WLD1003 motor is more effecient using 250g/Kwh at 2500 rpm verses the little air cooled single's 280g/Kwh at 2900 rpm.
2) Comparisons are at maximum effort - 55mph/3600rpm for the Enfield and 75/3000rpm for the Tiger
3) A litre of diesel fuel weight 0.862kg

So my predictions are:

85mph top speed in favorable conditions.
It should return 107mpg overall.

So it's up to you lot to keep me honest and see what turns out to be the real figures.

Cheers
Dave

[sbrumby]

I would think your calculations are about right, as mine are
6hp 41mph 225mpg
15hp 60mph 150mpg
23hp 70mph 120mpg.
the last one would go faster if geared different but that would be at the expence of acceleration & I am quite happy with 70mph.

[andrewaust]

Yes, no argument here either , sounds about right.

I find hot weather "bringing thin air conditions" absolutely kills the power and economy of the diesel.

One just has to wind the throttle back and enjoy max speeds of 85kph.

Best conditions will see 110kph. I'd have to convert metric to imperial for fuel comparisons, looking at your figures seems right from quick calculations.




A;)

[oilburner]

Here's an interesting different take on the actual average horsepower of your single cylinder Lombardini, based on the average 140 miles per gallon fuel consumption on the motorway. I've converted everything to imperial measure for all us old farts. The weights / measures and conversion formulas used for grams/lbs, kw/hp, etc. are from the Third Edition of Thomas Glover's Pocket Ref.

Lombardini BSFC (Brake Specific Fuel Consumption)
300 grams / 0.661386 lb per kw per hr
0.493195 lbs per hp per hr
(1 gram = .002205 lbs, 1 kw = 1.3410220896 hp)

Weight of Diesel Fuel
1 cu ft diesel fuel weighs 52.1 lbs
1 cu ft = 7.48052 us gallons
= 6.22902900 imp gallons
(1 us gal = 0.8327 imp gal)
1 imp. gal diesel fuel = 8.36406 lbs

Actual Fuel Consumption
140 mpg (55 mph on Motorway) = 140 mpg

140 miles = 2.54545 hrs, 8.36406 lbs fuel

Fuel consumed in 1 hr = 3.285886 lbs

Actual Average Horsepower
Fuel used in 1 hour divided by 0.493195 lbs per hp per hr
6.6624 horsepower

This closely agrees with the simple rule of thumb formula that I use to calculate speed for a given horsepower [mph = cube root of hp * 30] and conversely i.e. horsepower required for a given speed [cube of (mph/30)] which works out as follows:

55 mph divided by 30 = 1.8333
The cube of 1.8333 is 6.161700 horsepower

My $0.02CDN

[jeremy]

That bodes better for my (supposedly) 6.8 hp Hatz 1B30, doesn't it?

How come nobody is including "in-the-real-world" all-up weight in this discussion? I understand that this feedback as well as the theoretical work you all are doing all refer to findings based on your real-world experience on your own bikes, but what if the test platform were lighter, given the same hp? (and what does a Lombardini/Bullet actually weigh?)

I have been trying to keep my outcome as minimal as I can in the weight department, given the very limited 'oompf' of the powerplant--hopefully in the 250-280 lb. region. Fairings have been discussed as a good consideration in the top-speed equation as well, given the havoc that wind resistance wreaks.

[sbrumby]

Giving the weight of the bike is no problem, but the all up weight gives away how many pies have been eaten.

[roodesign]

This is very interesting to me..for my project...www.roopod.com, and I am so glad to get any figures about hp-mph ...that being said...is not the other question...acceleration? you need so many hp to go so fast...but what about how long it takes to get there? I imagine rider/bike weight plays more of a part in the accel bit, and also hill climbing...I think that the hp-mph equation is more about wind/rolling resistance, weight not so much...

my 2c

ps I would love to know your acceleration/ weight numbers? thanks for the info!
Roo

[Diesel Dave]

As regards acceleration this is the most difficult to measure as it needs to be accurate and quite impossible to do on your own.

Weight is the biggest factor in limiting acceleration and whilst a Bullet is not a heavy proposition, it's certainly no lightweight. the petrol 500 supposedly weighs in al 168 kilo's and my diesel is lighter than that.

There flywheel weight limiting factor too as a 28lb flywheel is not going to accelerate very quickly.

Best way to speed up acceleration must therefore be to dump all extra weight (especially rolling weight like steel rims) and shave the flywheel (but that's another arguement that has raged before.

Keep the faith
Dave

[Sibbo]

Dave,it seems that some form of aerodynamic fairing would improve those numbers markedly ,a very large amount of the engines output goes into pushing air out of the way .It looks like 80% in the graph below , cars are far more aerodynamic .


from http://www.velomobiel.nl/allert/Recumbe ... orbike.htm

[pietenpol2002]

I do recall from my training in the aviation world that to double your speed, you must quadruple your power. And no rolling resistance there - all parasitic drag. Evidence of the importance of streamlining.

[Sibbo]

Here's a table from a 1992 'Classic Motorcycle Magazine ',an article about a Dreamliner fairing mounted on a 13 hp 350cc petrol Enfield. Reducing wind resistance reduced fuel consumption ,increased top speed and acceleration .The fairing added an extra 45 pound .

[Mouse]

There are (were?) some very complex spreadsheets on a Yahoo diesel bike group that covered estimated top speed that I've had a play about with that take into consideration the manufactures fuel consumption values and a whole host of other stuff.


For comparison my 1900c single gear gives.
MPH MPG(UK)
50 95
70 80
80 70 or lower

also returns 75mpg when I'm pulling a trailer with a large dog in it

I'm sure the engine would be more efficient at lower rpm but that's the compromise of not having a gearbox.