# Willan's line

1. Dec 25, 2009

### monty37

how do we calculate friction power from the graph of total fuel consumption versus brake power?

2. Dec 25, 2009

### Bob S

You can't. BSFC (brake specific fuel consumption) depends on many things, including torque, valve timing, Otto cycle efficiency, spark timing (in SI engines), RPM, coolant temperature, etc. The best you could do is use the BSFC fuel consumption rate at zero torque output. But the fuel consumption rate is measured per kilowatt-hour output, which of course is zero at zero torque output. So for every RPM, plotting the fuel consumption rate vs. torque, and extrapolating to zero torque is a possibility. But this will not account for the increased friction in connecting rod bearings etc. when the MEP (mean effective pressure) or BMEP is higher. See
http://en.wikipedia.org/wiki/Mean_effective_pressure
All of the input energy has to go someplace. These are exhaust mass, velocity, temperature, coolant mass flow and temperature, accessory power, and of course brake power. How do you separate friction from everything else?
[added] see Fig. 5 on page 13 of
http://sitemaker.umich.edu/mhross/files/fueleff_physicsautossanders.pdf
But the zero intercept does not include all friction that is dependent on MEP.
Bob S

Last edited by a moderator: Apr 24, 2017
3. Dec 26, 2009

### monty37

i conducted a performance test on a single cylinder CI engine with various loads
i have only the brake power and total fuel consumption values with me.
so you think i cant find friction power directly from tfc but by finding BSFC,i can find.
but i have been asked to find friction power only using TFC and BP .

4. Dec 26, 2009

### Bob S

Last edited by a moderator: Apr 24, 2017
5. Dec 29, 2009

### brewnog

Haven't looked at Bob's links, but this is relatively straightforward. As with the title of your post, plot a Willans line (brake power vs fuel mass consumption from a part load curve) and extrapolate back to fit your data (I usually find a second order fit is adequate). Your part load data will need to be fairly thorough; I tend to run ten or so modes to fill this out nicely. To split out just where your energy input has gone at zero load will require you to look at the heat balance through the part load curve.

6. Dec 31, 2009

### monty37

i plotted the curve and got friction power at 7,giving me a mech efiiciency of 11%.
our teacher feels this is wrong as mech efficiency has to be around 70%.there is'nt any other method to find friction power?

7. Jan 1, 2010

### brewnog

The method is sound, you've got an error somewhere (measurement, calculation, or finger trouble).

Show your measured and calculated values and we'll have a look where the problem lies.

8. Jan 1, 2010

### Bob S

Most automobile CI engines are run at a 15% to 20% overall efficiency during normal driving conditions. Most of the inefficiency is due to thermodynamic limits (Otto cycle), but friction (e.g., pistons) contributes some additional losses. An automobile engine run at the "sweet spot" (about 35% of redline, 80 % of maximum torque) in the BSFC map can achieve over 30% total efficiency. In a BSFC plot, about 82 grams of petrol per kWh is equivalent to 100% efficiency; 250 grams per kWh is about 33%.
Bob S

Last edited: Jan 1, 2010
9. Jan 2, 2010

### monty37

s1 s2 time for 10cc exhaust temp outlet temp
5 0 49 99.5 36
10 0.5 33 120 37
15 1 30 160 38

Here s1 and s2 refer to the spring balance readings,and time for 10cc.
Based on this we calculate brake power,total fuel consumption,
Specific fuel consumption per hour,friction power and various efficiencies.
While TFC=(10/49)x0.835x(3600/1000)kg/hr;here 0.835 is density of fuel

from my calculations i got B.P :(Kw)
0.8919
1.694
2.4973

from my calculations for TFC:(kg/hr)
0.668
0.7515
0.835

Last edited: Jan 2, 2010
10. Jan 3, 2010

### brewnog

What have you used for your fuel calorific value? What have you used for your Cp for exhaust gas? Have you done your heat balance? Let's see it!

11. Jan 4, 2010

### monty37

i used 45300 kJ/kg as the calorific value(given data).why to use Cp at all for the exhaust gas.i did not do heat balance ,as that is a separate experiment for us,as this is performance test.

#### Attached Files:

• ###### engine.xls
File size:
13.5 KB
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158
12. Jan 4, 2010

### brewnog

I can't see any calculations there, just the values you posted earlier, did you upload the right file?

If you're not calculating a heat balance, how were you expecting to derive your friction power? You won't know how much of the energy you're putting in as fuel ends up in the exhaust or coolant, or what's used for pumping and ancilliaries.

13. Jan 4, 2010

### monty37

sorry , here are the calculations.

As you say,we never did heat balance ,we were asked to get FP from graph.

#### Attached Files:

• ###### calc.txt
File size:
692 bytes
Views:
126
14. Jan 12, 2010

### monty37

well , may i know how to proceed with this,as i have also shown calculations.

15. Jan 16, 2010

### monty37

i have checked my calculations and
all of those ridiculous answers,but can someone tell me where lies the error?
is it the friction power?
what if i find Friction power using Morse method?

16. Jan 17, 2010

### brewnog

Sorry I didn't look at this sooner.

To help with this, I need to see your full spreadsheet. I need to see your measured data (load = 5, 10 and 15 is meaningless). Seeing your graphs would help too, but just posting a few figures and a few calculations (without annotation or source of the data) makes things very difficult to review. I can't see how you've got friction power at 7kW. What I can see is that your brake power looks very low, so obviously your efficiency measures will naturally be poor.

We can help, but make things easy for us, we weren't there when you typed those calculations in and we weren't there when you ran the test!