## Distance for an IC engine for a given load

Hi,

I have this question that, how do we calculate the distance an IC engine can propel a vehicle for given certain conditions? And what would be those required certain conditions?

As a test case, i was looking at this engine:
http://www.yanmar.com.au/industrial/la_series/l48ae.htm

now, from the performance curve given, i took the RPM approx 3200, for which the bsfc is approx 0.26 Kg/KWh and Power is 3kW.
Fuel is gasoline (density=0.74616 Kg/L , CV=42900 KJ/kg)

so, the brake thermal efficiency = 1 / (bsfc x CV ) [units adjusted] = 0.32 = 32 %
now, as the engine is giving 3 KW of (assuming continuous) power, the input energy from fuel is = 3 / 0.32 = 9.1KW = 9.1 KJ/s

as CV = 42900 KJ/kg, the fuel that comes in, or the mass flow rate of fuel is = 9.1/42900 = 0.0002 kg/s.

Now, firstly, are the calculations uptil now correct? Are the assumptions (like constant power for a vehicle) valid?

If yes, how do i proceed from here?

Thanks!

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 You cant really proceed to work out how far a car will travel until you know the wheel diameter, and drive ratios. Are you talking about how far it could go on a set amount of fuel, assuming steady conditions?
 right...what else is needed? wheel dia is 19" gear ratios, i know the one for the 4th is 1:1, and is compounded in the driveline by a factor of 3.4 main question is, how do these factors link up with what i need? Yes, i am talking about how far it ll go on a set amount of fuel (1 L to be precise).

## Distance for an IC engine for a given load

You work out the distance and speed travelled from:

engine rpm*drive ratio*wheel circumfrence.

From speed and distance you get a time and power. you can then find how long the fuel will last by bsfc (EDIT: which you appear to have done already).

You can then work it back to find total distance.

You could also use your calcualtion of fuel used per seconf to find out how many seconds the engine will run. And work out speed and distance in the same way.

 Recognitions: Gold Member Science Advisor don't forget road surface, paved ? mud/ dirt? is ti flat? any hills in this scenario. also wind, temperature, humidity aero dynamics too... one more thing is diameter of drive wheels with driver and fuel. what does this pig weigh?

 Quote by xxChrisxx You work out the distance and speed travelled from: engine rpm*drive ratio*wheel circumfrence.
umm...you sure this is applicable here? I mean it is useful, as i have tried, to set a limit to the max speed the vehicle will travel for a set rpm and wheel dia, by altering the drive ratio? No?
 Quote by xxChrisxx From speed and distance you get a time and power. you can then find how long the fuel will last by bsfc (EDIT: which you appear to have done already). You can then work it back to find total distance. You could also use your calcualtion of fuel used per seconf to find out how many seconds the engine will run. And work out speed and distance in the same way. EDIT: This is only valied for steady load and conditions.
However, i was not able to get anything with dimensions of distance (apart from the wheel radius) in my calculations...am i doing it all wrong here?

Here is what i tried after the relations in the original post:
mass flow rate of fuel = 0.0002 kg/s
(Volume) flow rate = mass flow rate / density = 0.0002 / .74616 = 0.000289 L/s
Total number of liters = 1
so time all the fuel lasts = 1/0.000289 = 3462.3s = 57.7 mins

is this right?

 Quote by Ranger Mike don't forget road surface, paved ? mud/ dirt? is ti flat? any hills in this scenario. also wind, temperature, humidity aero dynamics too... one more thing is diameter of drive wheels with driver and fuel. what does this pig weigh?
hi ranger mike, and thanks!

i was wondering if these things come into play. For these calculations (which are pretty crude), i am assuming a lot of things just to get an idea of what mileage i can get, so these are the assumed values:
Coefficient of Drag = 0.2
Coefficient of Rolling Resistance = 0.03
Mass of the vehicle = 200 kg
And neglecting the grade, and other natural factors like wind, humidity, temperature.

with these values, the power requirements at around 35-40 km/h (which is the desired max speed) come out to be somewhere between 0.8-1 kW. (the engine i have mentioned has significantly higher max power, but i am just making approx calcs)

 Before we go any futher, what is the application?
 Recognitions: Gold Member Science Advisor good start! and yes..anytime you are moving..you are moving air..imagine a curtain that weight 14 pounds per square inch, stick your hand out the car window when moving 25 MPH. what kind of ground clearance can you get away with....lower the better to keep air out from under the vehicle. being old ..ancient school..what the H??? is KM/H... how much horsepower is that??? your CDs seems a little low..check out the attached.. a 440 pound car to me should not have that much rolling resistance..are you running disc brakes on all four corners? with that low a weight you can loose the disc brake pad drag and go with drum brake and shoes ifin you want to really go for the MPG numbers..ifin you really want to trick out the set up, go super light on the rotating mass, wheels, tires, drive train..what kind of transmission...lot of parasitic drag on components..flywheel ..what diameter? drive shaft or half shafts? can you go carbon fiber? gun drill them? also regarding the IC,,can you u duct cold air to the intake? can you up the water temperature to 240 degrees F..more heat makes more HP..can you run synthetic oil and differential grease in it.. all these will increase HP or fuel mileage. Attached Thumbnails
 Hang on 200kg with a driver 40odd kph, lawnmower engine... you're building a kart arent you? (seems a tad heavy for a road kart so maybe one of those offroad jobbies?) Also, to find the distane you will travel you have to use. rpm*ratio*circumfrence. Rpm * ratio gives the amount of time the wheel spins for each eagine revolution. So for example a drive ratio of 1:1 and engine speed of 3600 rpm, the wheel will rotate 3600times per min. The circumfrence of the tyre then lets you convert his angualr speed to a linear speed. So say we have a circumfrence of 1m. With 1m circumfrence, and a 1:1 drive ratio and 3600rpm. We travel 1 meter for every revolution. Or 3.6 km per min, which is a whopping 216 kmh. This means you will travel 205 km on 1 l of fuel in an hour. Now obviosly the figures are rubbish because you arent going to be using a 1:1 drive ratio or have a circumfrence of 1m. It just demonstrates the resoning behind the calc. Now if you've limited it to 40kph you'll go 0.95*40 miles on the fuel. Before you go complicating it with losses aich as drag and rolling resistance. Work it out as an ideal case, then make it more complicated. Then you can work out if you've got the power to do that speed.
 ok...the application is an energy-efficient mini-car for an event called eco marathon organized by Shell. In fact, we have talked about this here, and have been consulting with a book or two (as was told to do) since then. Ranger Mike, I sometimes find it difficult to understand certain portions of your messages, but always find them the most encouraging and helpful. Anyhow, - Minimum ground clearance the rules allow is 10 cm - Cd, 0.2, is a bit on the lower (and optimistic) side, but i did a small research on teams from previous years, and they did as low as 0.18 - Rolling resistance; wikipedia says 0.03 for 'ordinary tires on asphalt'. I guess this can be lowered (but i havent reached the tires chapter yet, so can't say for sure :-) ) There are supposedly some Michelin tires specifically for the event, but i haven't managed to find a tangible link. The e-shop from the organizers isn't up yet, so there's time still for that i guess - Disc brakes on all wheels necessary (the rules) - super-light rotating parts. Actually, we intend to use a 'branded' engine. The power required (assumed at the moment) to overcome drag and rolling resistance comes out to be around 0.8-1 kW. The track gradient is max 5%, which puts around 0.15 kW more required on certain sections. If we manage to arrange a carbon-fibre supplier, this could drop marginally (due to weight). So my teacher recommended to look up (not necessarily finalise) en engine twice that much power. So, there are a few i could locate: http://www.honda-engines.com/engines/gxv50.htm very high rpm, if my basics are correct, this would require a compound transmission ration of around 20 for speed limited to 36kph! http://www.honda-engines.com/engines/gx100.htm would require a compound transmission ratio of around 10 for the same speed. Now, i am also unable to get the complete performance curves (including the bsfc) for each. Obviously, these are not finalised, just on the table. We d be also looking at engines from the junk as well. If anyone has an idea of better ones, that ll be welcome. We d definitely have to make some changes to them, and i think ill be getting in touch with you soonif thats ok with you Chris, the relations are helpful...thanks! why did you multiply the final thing by 0.95??? couldn't get that part
 Oh yeah, I remember now. Sorry that was just a quick in the head calc, it came from the fact you said you had 57.7 mins of fuel (from your calcualtion) at that engine speed. So I just took the 57 mins out of the hour. so 57/60 is .95 However, for the ultra ecomomy, the way we;ve calcualted the fuel economy is going to be way way wrong for your needs. As we are calcualting the engine running at a constant 3600 rpm, which is putting out far too much power for your needs and is wasting tons of power and therefore vital fuel. 3 kw as opposed to the 1 you said you needed. If you are stuck with that motor, you may want to gear it so that you operate lower in the rev range (at the power output you need). Sacrificing specific fuel economy for less combustion events, giving an overall gain. Better yet pick a smaller motor. As I remember you are in a road going class, so its stop start. Is there a miminum accelration up to top speed required?
 Recognitions: Gold Member Science Advisor you find it difficult to understand me..??? so did my ex wife///ifin you are intending on winnin this let me know if some futile homework bs ok too but let me know cause this whole post can kick the dog do do out of the competition ifin you let um guys like fred and danger an xxchris etc...
 hey chris! No, we aren't stuck with that motor. in fact, its what one of the teams used 2 years back. They managed 91 km to the Litre. We are looking in the market (the net for makers like honda etc) and the local junks for smaller ones. As i posted above, the 50cc Honda one giving 1.6 kW at 7000 rpm comes the closest in the ones we have seen upto now. Secondly, there is no max speed specified. The event does say, that the vehicle must complete 6 legs of a 2.7 km track in a certain time (including about 3 pit stops of 10 secs each) the average speed for which should be 30kph at least. There is no mention of a minimum accelaration up to top speed, but obviously, all of it has to fit in the given time. Ranger Mike, winning this? thats going to be a long shot. here are the results from this year: http://www.shell.com/home/content/ec...ults_2009.html as you can see, the highest is a whopping 589 km/L, but many of these teams might not participate this year in asia. but that doesn't mean the bar will be much lower coz there are going to be good teams from here too. We ll try our best
 Recognitions: Gold Member Science Advisor it looks challenging..are you the main wrench bender or are you the design wizard on this team? how many crew do you have? give us some background
 hmm...thats an interesting one! At the moment, i am the design (not-so-wizard) person in the team. We have a person from electrical engineering, and he is working on the electrical systems (the lighting, horns) Then there is a person from mechatronics and four,five from mechanical [btw, all our going to start our third year]. At the moment, we have one person researching the previous years of this competition, trying to get as much data as available for the better teams. One-two guys will start on the chassis this week, with our teacher.

 Quote by xxChrisxx Now if you've limited it to 40kph you'll go 0.95*40 miles on the fuel. Before you go complicating it with losses aich as drag and rolling resistance. Work it out as an ideal case, then make it more complicated. Then you can work out if you've got the power to do that speed.
So what basically, what this means is, and thats the rresult i have been getting in my calcs btw, that whatever mileage i will get will be:
mileage = vehicle speed x time it takes for the engine to burn 1 L

so,
1. if we make the max speed go to, say hypothetically, 200 kph, for the engine we have discussed, i get 200 x 0.95 = 190 km/L?!!!!
2. i actually think there would be more to this. What i mean here is that the organizers have put a limit to the min. speed (30 kph (average)) so i infer from this is that mileage is inversely related to speed: i.e more speed=>less mileage and vice-versa. Umm???

Second, you have said to 'work it out as an ideal case' before making it more complicated. What would be the ideal case here? (i thought that by eliminating all those factors like drag etc, this is the ideal case; not sure) ?

Thanks!

 Well... its more complicated than that. The equation we used is very very basic, and highly simplified. Our calculation shows that the faster you go the better milage you get. This is only valied for a linear region, where the power requirements are low. So for example, take the engine you showed in the link. If you geared it to go 10 miles in 1 hour we would be getting 10mpl. If you geared it to 20 miles in 1 hour, you would be getting double the fuel milage. This is valid becuase the engine is producing enough power for both speeds to be viable. Going at 160odd mph requires much much more power than the egnine can provide, so the equation we used is not valied. What you need to do is to find a speed you want to go, ideally the minimum speed you can get away with, to reduce power requirements. Add in losses. This gives you the minimum power requirement to perform the task. You then find the engine with the lowest specific consumtion at this speed. I'm busy atm, i'll come back and answer this more thoroghly at some point.