Longitudinal Vehicle Dynamics and Performance
Comprehensive university textbook unit covering fundamental principles, governing relationships, and engineering applications of Longitudinal Vehicle Dynamics and Performance.
§2.1 Whole-vehicle free-body analysis
**Learning objective.** Build a reproducible analysis of **force accounting on a consistent inertial basis**, then evaluate whether identify required tire force. The illustrative field case is **an accelerating delivery van**. The primary relation is `F_wheel - F_drag - F_roll - F_grade = m*a`; it is a starting approximation, not a complete calibration or certification method.
§2.2 Power-limited acceleration
**Learning objective.** Build a reproducible analysis of **traction force versus shaft power as vehicle speed changes**, then evaluate whether choose a feasible motor and gearing envelope. The illustrative field case is **a launch that transitions from tire-limited to power-limited**. The primary relation is `P_wheel = F_wheel*v`; it is a starting approximation, not a complete calibration or certification method.
§2.3 Gradeability and tire traction
**Learning objective.** Build a reproducible analysis of **traction available from the driven axle or wheel**, then evaluate whether assess uphill launch without wheel slip. The illustrative field case is **a rear-wheel-drive vehicle starting on a hill**. The primary relation is `F_max = mu*F_normal`; it is a starting approximation, not a complete calibration or certification method.
§2.4 Relative wind and road-load power
**Learning objective.** Build a reproducible analysis of **air-relative resistance multiplied by road-relative travel speed**, then evaluate whether select a test speed and wind correction. The illustrative field case is **a highway drive into a sustained headwind**. The primary relation is `P_aero = 0.5*rho*Cd*A*v_rel^2*v_vehicle`; it is a starting approximation, not a complete calibration or certification method.
§2.5 Energy consumption and duty-cycle decomposition
**Learning objective.** Build a reproducible analysis of **positive propulsion work and negative braking work**, then evaluate whether quantify effects of mass versus aerodynamics. The illustrative field case is **stop-and-go courier duty cycle**. The primary relation is `E_wheel = integral(F_wheel*v*dt)`; it is a starting approximation, not a complete calibration or certification method.
Step-by-Step Automotive Engineering Solutions
Three original questions connect calculations, definitions and interpretation. Open each solution to follow the reasoning.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Whole-vehicle free-body analysis** under steady operational loading.
Worked Engineering Derivation:
For mass 1700 kg, acceleration 1.5 m/s² and combined resistance 360 N, F_wheel = 1700×1.5 + 360 = 2910 N. This is a demand, not a claim that the vehicle can actually develop that tire force. **Cross-check:** Reconstruct the result from the stated inputs without rounding intermediate values prematurely. Describe which term would change if the test were repeated with a new vehicle mass, ambient temperature or tire configuration. At least one check should concern the scale of the result: compare the derived force with vehicle weight, the energy with a known kinetic-energy change, or the speed with a plausible road operating point. A result can satisfy the formula exactly and still be inapplicable because one assumption is not true.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Power-limited acceleration** under steady operational loading.
Worked Engineering Derivation:
To maintain 3000 N wheel force at 20 m/s requires 60 kW at the wheels. At 30 m/s, the same force requires 90 kW, before gearbox and motor losses; a 60 kW-limited design cannot maintain that force. **Cross-check:** Reconstruct the result from the stated inputs without rounding intermediate values prematurely. Describe which term would change if the test were repeated with a new vehicle mass, ambient temperature or tire configuration. At least one check should concern the scale of the result: compare the derived force with vehicle weight, the energy with a known kinetic-energy change, or the speed with a plausible road operating point. A result can satisfy the formula exactly and still be inapplicable because one assumption is not true.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Gradeability and tire traction** under steady operational loading.
Worked Engineering Derivation:
If a driven axle supports 8000 N normal load and assumed peak friction is 0.7, the illustrative total longitudinal force bound is 5600 N. The simple product is not a guaranteed tire force on an actual road. **Cross-check:** Reconstruct the result from the stated inputs without rounding intermediate values prematurely. Describe which term would change if the test were repeated with a new vehicle mass, ambient temperature or tire configuration. At least one check should concern the scale of the result: compare the derived force with vehicle weight, the energy with a known kinetic-energy change, or the speed with a plausible road operating point. A result can satisfy the formula exactly and still be inapplicable because one assumption is not true.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Relative wind and road-load power** under steady operational loading.
Worked Engineering Derivation:
At F_drag = 300 N and ground speed 25 m/s, road-load power is 7.5 kW, even if relative airflow is faster than 25 m/s because of wind. **Cross-check:** Reconstruct the result from the stated inputs without rounding intermediate values prematurely. Describe which term would change if the test were repeated with a new vehicle mass, ambient temperature or tire configuration. At least one check should concern the scale of the result: compare the derived force with vehicle weight, the energy with a known kinetic-energy change, or the speed with a plausible road operating point. A result can satisfy the formula exactly and still be inapplicable because one assumption is not true.
Problem Statement: An engineering practitioner analyzes a mechanical system governed by **Energy consumption and duty-cycle decomposition** under steady operational loading.
Worked Engineering Derivation:
A 1600 kg vehicle accelerated from rest to 15 m/s gains 0.5×1600×15² = 180,000 J = 0.050 kWh of translational kinetic energy. Ideal energy recovery cannot exceed that amount for this single acceleration–braking event. **Cross-check:** Reconstruct the result from the stated inputs without rounding intermediate values prematurely. Describe which term would change if the test were repeated with a new vehicle mass, ambient temperature or tire configuration. At least one check should concern the scale of the result: compare the derived force with vehicle weight, the energy with a known kinetic-energy change, or the speed with a plausible road operating point. A result can satisfy the formula exactly and still be inapplicable because one assumption is not true.