Now consider a representative sport-utility vehicle (SUV) also with five-passenger capacity. The SUV rides higher off the road, and so has a larger frontal area of 3.1 m^2 and a higher drag coefficient of 0.4. Due to more rugged tires, the rolling resistance coefficient increases to 0.015. The curb

Question

Now consider a representative sport-utility vehicle (SUV) also with five-passenger capacity. The SUV rides higher off the road, and so has a larger frontal area of 3.1 m[latex]^2[/latex] and a higher drag coefficient of 0.4. Due to more rugged tires, the rolling resistance coefficient increases to 0.015. The curb weight is higher at 1500 kg, but the power train is also stronger, delivering a maximum tractive force at low speeds of 4500 N, and tractive power at maximum speed of 50 kW. (In standard units, the vehicle has a cross-sectional area of 33.4 ft[latex]^2[/latex] and weighs 3300 lb.) (a) Calculate the cruising power requirement at 96 km/h; the maximum speed; and the maximum gradability. (b) Suppose both the SUV and the economy car in Example 13-1 accelerate from a standstill at full force in a frictionless vacuum, and that they can maintain the maximum low-speed tractive force over the entire range of speeds. How fast will each of them reach the cruising speed of 96 km/h or 60 mph?

Accepted Answer

(a) Repeating the calculations from Example 13-1 but using new parameters for the SUV, the answers are P[latex]_{TR}[/latex] = 17.6 kW, V[latex]_{max}[/latex] = 146 km/h (91.0 mph), and GR[latex]_{max}[/latex] = 32.2%.

(b) Since there is no resistance and tractive force is constant, we can apply Eq. (13-3) to the case of both vehicles. For the car:

[latex]A_{\max }=\frac{F_{\mathrm{TR}}}{m}[/latex] (13-3)

[latex]A_{\max }=\frac{F_{\mathrm{TR}}}{m}=\frac{3000}{1200}=2.5 \mathrm{~m} / \mathrm{s}^{2}[/latex]

In order to reach cruising speed of 26.7 m/s, the car must accelerate for t = (26.7)/(2.5) = 10.7 s. By similar calculation, for the SUV, A[latex]_{max}[/latex] = 3 m/s[latex]^2[/latex], t = (26.7)/(3) = 8.9 s. Note that because the assumptions about vehicle specifications are simplistic, the comparison is not transferable to actual vehicles having approximately the same dimensions.

Discussion A comparison of the results for the two vehicles is given in the table below. The percent change column gives the percent change up or down for the value for the SUV, relative to that of the car.

	Units	Compact	SUV	Change
Cruise	kW	10.5	17.6	67%
Maximum speed	Km/h	144.6	145.7	1%
	mph	90.4	91.0	1%
Gradability	percent	26.40%	32.20%	22%
Acceleration	seconds	10.7	8.9	−17%

Question 13.2: Now consider a representative sport-utility vehicle (SUV) al...

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