This section describes the reference method for calculating drag area, CdA, for tractors using coastdown testing. Follow the provisions of Sections 1 through 9 of SAE J2263 (incorporated by reference, see § 1037.810 ), with the clarifications and exceptions described in this section. Several of the exceptions in this section are from SAE J1263 (incorporated by reference, see § 1037.810 ). The coastdown procedures in 40 CFR 1066.310 apply instead of the provisions of this section for Phase 1 tractors.
Where:
w = filtered wind speed.
v = filtered vehicle speed.
øw = filtered wind direction. Let øw = 0° for air flow in the first travel direction, with values increasing counterclockwise. For example, if the vehicle starts by traveling eastbound, then øw = 270° means a wind from the south.
øveh = the vehicle direction. Use øveh = 0° for travel in the first direction, and use øveh = 180° for travel in the opposite direction.
Example:
w = 7.1 mi/hr
v = 64.9 mi/hr
øw = 47.0°
øveh = 0°
vair,th = 69.93 mi/hr
Example:
w = 7.1 mi/hr
v = 64.9 mi/hr
øw = 47.0°
øveh = 0°
[PSI]air,th = 4.26°
Where:
Me = the vehicle's effective mass.
v = average vehicle speed at the start or end of each speed range, as described in paragraph (h)(3) of this section.
t = timestamp at which the vehicle reaches the starting or ending speed expressed to at least one decimal place.
M = the vehicle's measured mass.
ag = acceleration of Earth's gravity, as described in 40 CFR 1065.630 .
h = average elevation at the start or end of each speed range expressed to at least two decimal places.
D = distance traveled on the road surface from a fixed reference location along the road to the start or end of each speed range expressed to at least one decimal place.
Example:
Me = 17,129 kg (18 tires in contact with the road surface)
vstart = 69.97 mi/hr = 31.28 m/s
vend = 59.88 mi/hr = 26.77 m/s
tstart = 3.05 s
tend = 19.11 s
M = 16,108 kg
ag = 9.8061 m/s2
hstart = 0.044 m
hend = 0.547 m
Dstart = 706.8 ft = 215.4 m
Dend = 2230.2 ft = 697.8 m
F = 4645.5 N
Where:
vseg[speed] = the mean vehicle speed of all vehicle speed measurements in each low-speed and high-speed segment.
TRPM = tire revolutions per mile for the drive tire model installed on the tractor being tested according to § 1037.520(c)(1) .
Example:
vseghi = 28.86 m/s
vseglo = 5.84 m/s
TRPM = 508 r/mi = 0.315657 r/m
c0 = -206.841 W
c1 = 239.8279 W·s/r
c2 = 21.27505 W·s2/r2
Fspinhi = 129.7 N
Fspinlo = 52.7 N
[DELTA]Fspin
Eq. 1037.528-10
Example:
[DELTA]Fspin
= 77.0 N
Step Number | Load (% of max) | Inflation pressure (% of max) |
1 | 20 | 100 |
2 | 55 | 70 |
3 | 85 | 120 |
4 | 85 | 100 |
5 | 100 | 95 |
Where:
nt,[axle] = number of tires at the axle position.
p[axle] = the inflation pressure set and measured on the tires at the axle position at the beginning of the coastdown test.
L[axle] = the load over the axle at the axle position on the coastdown test vehicle.
[ALPHA][axle], [BETA][axle], a[axle], b[axle], and c[axle] = regression coefficients from SAE J2452 that are specific to axle position.
Example:
nt,steer = 2
psteer = 758.4 kPa
Lsteer = 51421.2 N
[ALPHA]steer = -0.2435
[BETA]steer = 0.9576
asteer = 0.0434
bsteer = 5.4·10-5
csteer = 5.53·10-7
nt,drive = 8
pdrive = 689.5 kPa
Ldrive = 55958.4 N
[ALPHA]drive = -0.3146
[BETA]drive = 0.9914
adrive = 0.0504
bdrive = 1.11·10-4
cdrive = 2.86·10-7
nt,trailer = 8
ptrailer = 689.5 kPa
Ltrailer = 45727.5 N
[ALPHA]trailer = -0.3982
[BETA]trailer = 0.9756
atrailer = 0.0656
btrailer = 1.51·10-4
ctrailer = 2.94·10-7
vseghi = 28.86 m/s = 103.896 km/hr
vseglo = 5.84 m/s = 21.024 km/hr
FTRRhi,steer = 365.6 N
FTRRhi,drive = 431.4 N
FTRRhi,trailer = 231.7 N
FTRRlo,steer = 297.8 N
FTRRlo,drive = 350.7 N
FTRRlo,trailer = 189.0 N
Example:
FTRRhi = 365.6 + 431.4 + 231.7 = 1028.7 N
FTRRlo = 297.8 + 350.7 + 189.0 = 837.5 N
Where:
Tseg[speed] = the average ambient temperature during the coastdown segment, in °C.
Example:
FTRRhi = 1028.7 N
FTRRlo = 837.5 N
Tseghi = 25.5 °C
Tseglo = 25.1 °C
FTRRhi,adj = 1 + 0.006·(24-25.5)] = 1019.4 N
FTRRlo,adj = 837.5·[1 + 0.006·(24-25.1] = 832.0 N
Example:
[DELTA]FTRR = 1019.4-832.0 = 187.4 N
Where:
Fhi = road load force at high speed determined from Eq. 1037.528-7.
Flo,pair = the average of Flo values for a pair of opposite direction runs calculated as described in paragraph (h)(8) of this section.
[DELTA]Fspin = the difference in drive-axle spin loss force between high-speed and low-speed coastdown segments as described in paragraph (h)(5) of this section.
[DELTA]FTRR = the difference in tire rolling resistance force between high-speed and low-speed coastdown segments as described in paragraph (h)(6) of this section.
v2air,lo,pair = the average of v2air,lo values for a pair of opposite direction runs calculated as described in paragraph (h)(8) of this section.
R = specific gas constant = 287.058 J/(kg·K).
T = mean air temperature expressed to at least one decimal Place.
Pact = mean absolute air pressure expressed to at least one decimal place.
Example:
Fh i = 4645.5 N
Flo,pair = 1005.0 N
[DELTA]Fspin = 77.0 N
[DELTA]FTRR = 187.4 N
v2air,hi = 933.4 m2/s2
v2air,lo,pair = 43.12 m2/s2
R = 287.058 J/(kg·K)
T = 285.97 K
Pact = 101.727 kPa = 101727 Pa
40 C.F.R. §1037.528