# PREDICTION OF FUEL CONSUMPTION

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2 Ratio of engine power to rated power Ratio of engine speed to rated speed Figure 1. Data points of which fuel consumption data were used for model development. Fuel Consumption (L/h) Engine power (kw) Figure. Fuel consumption vs. engine power at varying load with full throttle. between the fuel consumption and engine power known as a governor line of a given tractor may be expressed as: Q = ap + b (1) Q = fuel consumption at varying load with full throttle (L/h or kg/h), P = engine power (kw), a, b = constants representing respectively the slope and intercept of the line defined by equation 1. governor line with full throttle as shown in figure 3. It is noted from the figure 3 that the fuel consumption lines are almost parallel with each other, which means the fuel consumption increases linearly with engine power by the same increasing rate both at the full and reduced throttles although the intercept differs depending upon the opening of the throttle. The increasing rate of the governor line in figure 3 is L/kW h with a correlation coefficient greater than Those of the lines representing varying load at standard PTO speed, partial loads at 90% and 60% of rated speed are, respectively, 0.41, 0.45 and 0.33 L/kW h. Percentage errors of the increasing rates with respect to that of the governor line are 8.9%, 1.4%, and 5.5%, respectively. The fuel consumption data of the 15 tractors showed the same trend of the increasing rate with an average percentage error of 8.3%. In addition, a t test was conducted to test a null hypothesis that the increasing rates of fuel consumption at the standard PTO speed, 90% and 60% of rated speed are statistically equal to that of the governor line. For three increasing rates in figure 3, the calculated t value is: t = abs = Since this is less than the table value t 0.01, = at a probability of 1% with of freedom, we accepted the null hypothesis and concluded that the increasing rates are equal. The t values calculated from the 15 tractors ranged from to 3.1 which is also less than the table t value. It was concluded from this fact that the difference in fuel consumption at varying loads with full and reduced throttles is mainly due to speed difference regardless of the engine power level (Kim et al., 010). Based on this result, the fuel consumption at varying load with reduced throttle was assumed to have the same increasing rate as the governor line and estimated as follows. Suppose that fuel consumption at an arbitrary operational point A defined by an engine speed n A and its power P A is to be estimated using PTO power performance data. The PTO FUEL CONSUMPTION MODEL FOR VARYING LOAD WITH REDUCED THROTTLE It was assumed that the relationship between the fuel consumption and engine power at varying load with reduced throttle has the same trend as exhibited at varying load with full throttle on the basis that the governor controls the engine speed with the same characteristics of regulation regardless of the governor type; mechanical or electronic. This assumption may be accepted if the fuel consumption at varying load with reduced throttle varies linearly with engine power and its rate of change equals the slope of the governor line with full throttle. Fuel consumption data of a tractor taken at the standard PTO speed with full throttle and at the partial loads with reduced throttle (90% and 60% of the rated speed) were plotted as a function of engine power and compared with the Fuel consumption (L/h) Varying load at rated speed (governor line) Varying load at PTO standard speed Partial load at 90% of rated speed Partial load at 60% of rated speed Engine power (kw) Figure 3. Fuel consumption lines under different operating conditions. 706 APPLIED ENGINEERING IN AGRICULTURE

3 power performance data of an OECD tractor test report can be plotted as shown in figure 4. Step 1: Draw a straight line passing through point A and parallel to a line BD representing engine power as a function of speed ratio at varying load with full throttle as shown in figure 4. Let C be the interaction between the straight line and full load power curve. The straight line AC can be expressed as: P = a p ( n na) + PA () a p = slope of line BD in figure 4, P = engine power (kw), P A = engine power at operational point A (kw), n = ratio of engine speed to rated speed, n A = ratio of engine speed at operational point A to rated speed. Step : Determine the engine speed and power for the operational point C. The full load power data may be expressed as a quadratic equation as a function of engine speed ratio: P = k1n + kn + k (3) 3 P = engine power (kw), n = ratio of engine speed to rated speed, k 1, k, k 3 = constant coefficients. Solving equations and 3 for the speed, n C and power, P C yields: ( k a p ) + nc = ( k a p ) 4k1( k3 + a pna PA ) k1 P C = a p ( nc na) + PA (5) Step 3: Determine the fuel consumption at the point C using the full load fuel consumption curve. The full load fuel consumption data can also be expressed as a quadratic equation as a function of engine speed ratio: Q = s1n + sn + s (6) 3 Ratio of engine power to rated power Ratio of engine speed to rated speed Figure 4. Estimation of fuel consumption at operational point A. C A D B (4) Q = fuel consumption (L/h or kg/h), n = ratio of engine speed to rated speed, s 1, s, s 3 = constant coefficients. Then, the fuel consumption at the point C, Q C can be calculated as follows: QC = s1nc + snc Step 4: Determine the fuel consumption at the operational point D using equation 1. Since the same power is transmitted at the points C and D, that is, P D = P C the fuel consumption at the point D can be calculated as: QD = apc + b Step 5: Determine the difference between the fuel consumptions at points C and D. That is, QD Q C Step 6: As in step 4, determine the fuel consumption at the point B using equation 1. QB = apa + b Step 7: Determine the fuel consumption at point A from the fact that the difference between Q B and Q A equals the difference between Q D andq C. That is, QB QA = QD QC Then, the fuel consumption at the point A becomes: QA = QB QD + QC = a( PA PC ) + s1nc + snc Substituting equation 5 into the above equation gives a final model to estimate the fuel consumption at the operational point A as follows: Q A = s1 nc + ( s aa p ) nc + aa pn (7) A MODEL VERIFICATION To verify the validity of the prediction model, fuel consumptions were estimated using the model at following four operational points and compared with measured data given by the OECD test reports. Point 1 at which 80% of rated power is transmitted at 90% Point at which 40% of rated power is transmitted at 90% Point 3 at which 60% of rated power is transmitted at 60% Point 4 at which 40% of rated power is transmitted at 60% The fuel consumptions were also compared at varying loads with full throttle at standard PTO speed. Test reports of four tractor models MF7480, MXU15, MT45B, and MF8480 approved respectively as OECD Approval Numbers / 195(004), / 59(005), / 35(006) and / 34(005) were used for the validation. They are different from those used for the model development. Table 1 shows fuel consumption data of the Vol. 7(5):

4 Load Full load with reduced throttle Varying load at rated speed with full throttle Table 1. Data of fuel consumption and power of sample tractor (MF7480). Engine Speed Ratio Power Speed to Rated (kw) (rpm) Speed Fuel Consumption (kg/h) model MF7480 taken at full load with reduced throttle and at varying load with full throttle as an example. The coefficients of equation 1 were obtained by fitting the fuel consumption data at the varying load with full throttle into equation 1. A best regression was obtained with a correlation coefficient of R = when: Q = 0.103P (8) which yields a=0.103 and b= To determine the coefficient a p of equation, the engine power at varying load with full throttle was expressed as a linear function of speed ratio: P = n (R =0.9987) (9) which yields a p = Power and fuel consumption data taken at full load with reduced throttle were fitted into equations 3 and 6, respectively, resulting in: P =.09n n (R =0.9967) (10) Q = 4.039n n (R =0.9957) (11) Then, the coefficients of equations 3 and 6 are k 1 =.09, k =391.94, k 3 = , s 1 = 4.039, s =84.314, and s 3 = Since the rated speed and power of the sample tractor was 00 rpm and 86.7 kw, the speed ratios and engine powers of the operational points 1,, 3, and 4 are given as follows: (n 1, P 1 ) = (0.9, 69.3 kw) (n, P ) = (0.9, 34.8 kw) (n 3, P 3 ) = (0.6, 51.9 kw) (n 4, P 4 ) = (0.6, 34.8 kw) Fuel consumption at operational point 1 was estimated using equations 4 and 7 as follows: ( k a p ) + nc = = / { [ ( )] [ (.09) ] = ( k a p ) 4k1( k3 + a pn1 P1 ) k1 + [ ( )] 4(.09)[ ( )(0.9) 69.3] Q1 = s1nc + ( s aa p ) nc + aa pn1 = ( 4.039)(0.8874) + [ (0.103)( )] (0.8874) + ( ) + (0.103)( )(0.9) = kg/h Similarly, fuel consumptions at operational point, 3, and 4 are obtained as follows: Q = 1.43 kg/h Q 3 = kg/h Q 4 = 9.88 kg/h The percentage errors of the estimated fuel consumptions ranged from 3.51% to 8.3% at partial load with reduced throttle as shown in table. The same method was applied to estimate fuel consumptions at varying load with full throttle at standard PTO speed, of which percentage errors ranged from 0.69% to 4.67% as shown in table 3. The percentage errors of the predicted fuel consumptions for MXU15 ranged from 0.49% to 4.17% at varying load with full throttle at standard PTO speed and from 3.8% to 7.40% at partial load with reduced throttle. Those for MT45B and MF8480 were, respectively, 1.0% to 3.11% and Operational Point Table. Measured and estimated fuel consumptions at partial loads with reduced throttle for sample tractor (MF7480). Operational Condition Fuel Consumption Ratio of Engine Speed to Rated Speed Power (kw) (80% of rated power) (40% of rated power) (60% of rated power) (40% of rated power) Measured (kg/h) Estimated (kg/h) Percent Error (%) APPLIED ENGINEERING IN AGRICULTURE

5 Table 3. Measured and estimated fuel consumptions at varying load with full throttle at standard PTO speed for sample tractor (MF7480). Engine Speed Power Fuel Consumption (kg/h) Percent Error (rpm) (kw) Measured Estimated (%) % to.80% at varying load with full throttle at standard PTO speed, and.57% to 6.6% and 1.36% to 9.15% at partial load with reduced throttle. There was a tendency that larger errors occurred at 40% of rated power and 60% of rated speed with reduced throttle. The errors may be attributable to less accurate reading of the data at full load with reduced throttle given in a graphical form in the OECD test reports. There is also a possibility that measuring errors in the tractor test may cause the prediction errors. To reduce the prediction errors, more measured data of the test reports should be compared with model predictions and the model may need a further adjustment accordingly to reflect engine characteristics of tractor. Until that time, the method developed in this study may be used to estimate the fuel consumptions of a given tractor at any operational conditions using its OECD tractor test data. SUMMARY AND CONCLUSIONS This study was conducted to develop a mathematical method to predict fuel consumption of agricultural tractors under any operational conditions using OECD tractor test data. The method is based on the assumptions that the fuel consumption at varying load with full throttle are linearly proportional to power, and the difference in fuel consumptions at varying load with full and reduced throttles are equal regardless of engine power level if their speed difference is the same. The average percentage errors of the predicted fuel consumptions for the selected four tractor models ranged from 0.11% to 4.69% at varying load with full throttle at standard PTO speed and from 1.36% to 9.15% at partial load with reduced throttle. Although the prediction model needs a further improvement, the method developed in this study may be used to estimate reasonably the fuel consumptions of a given tractor under various operational conditions. Following are the results of this study: Fuel consumption at varying load with full throttle is linearly proportional to power. Difference in fuel consumptions at varying load with full and reduced throttles is equal regardless of power level if their speed difference is the same. Fuel consumption at any operational conditions may be estimated reasonably well by using the prediction method developed in this study. ACKNOWLEDGEMENTS This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (KRF D01344). REFERENCES Cemagref Test report No OECD restricted code test of an agricultural tractor Antony cedex France. DLG Testing Station for Agricultural Machinery Report on test accordance with OECD standard code for the official testing of agricultural and forestry tractor performance. OECD Approval No. / 195. D 6483 Gross Umstadt, Germany. DLG Testing Station for Agricultural Machinery Report on test accordance with OECD standard code for the official testing of agricultural and forestry tractor performance. OECD Approval No. / 34. D 6483 Gross Umstadt, Germany. Goering, C. E., M. L. Stone, D. W. Smith, and P. K Turnquist. 00. Off road Vehicle Engineering Principles. St. Joseph, Mich.: ASAE. Grisso, R. D., D. H. Vaughan, and G. T. Roberson Fuel prediction for specific tractor models. Applied Eng. in Agric. 4(4): Harris, H. D., and F. A. Pearce A universal mathematical model of diesel engine performance. J. Agric. Eng. Res. 47: Harris, H. D Prediction of tractor engine performance using OECD standard test data. J. Agric. Eng. Res. 53: Kim, S. C., K. U. Kim, and D. C. Kim Modeling of fuel consumption rate for agricultural tractors. J. Biosystems Eng. 35(1): 1 9. OECD Standard code the official testing of agricultural and forestry tractor performance. Paris, France: OECD. Silsoe Research Institute OECD restricted standard code for the official testing of agricultural and forestry tractor performance. OECD Approval No. / 59. West Park Silsoe, UK: Silsoe Research Institute. Vol. 7(5):

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