Dynamics of a car/airplane

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Presentation transcript:

Dynamics of a car/airplane and fuel economy: Part II

Q1 A car moving with 80km/hr on a highway; the work done by thrust force is mainly to 1) fight against the rolling-friction force; 2) against the air drag; 3) against both; 4) acquire additional kinetic energy.

Q2 A car is accelerated to 50km/hr within 5s; the work done by thrust force is mainly to 1) fight against rolling-friction forces; 2) against the air drag; 3) against both; 4) Acquire desired kinetic energy.

Q3 At 80km/hr, the rolling-friction force and air drag are about equal. And a car consumes 6L/100km at this speed. How much it consumes per 100km if its speed is 120km/hr. (Engine efficiency is assumed to be independent of speed.) 10L; 14L; 3) 18L; 4) 20L.

Summary of dynamics of a car W(net)=W (thrust) – W(friction, Drag)= DK W(thrust) =W(friction, Drag)+ DK During cruising at constant speed, DK=0; 2) Acceleration costs extra energy!! 3) Fuel economy/100km: Efficiency X ( # of L) X (32MJ/L) =Work (thrust)

Hybrid Cars Why are hybrid cars more energy efficient? Efficiency of combustion engines depends on rpm. Most efficient at relative high speeds ~ 90 km/h. Electric motor very efficient at all speeds.

Energy needed to climb up to an altitude of 10.5km The mass of the plane is 390 000 kg at take-off. V= m g h = 4 x 10^10 J Kinetic energy at the cruising speed of 915 km/h (254 m/s). K = ½ m v^2 = 1.26 x 10^10 J How much fuel is needed for this? The energy efficiency of the jet engines is ~25% (estimated) Energy in jet fuel: 37.6 MJ/L. So we need 1400 L/0.25 = 5600L of jet fuel to accelerate to 915 km/h and go up to 10500 m.

Fuel Economy of Airplanes A Boing 747 has a maximum range of 13,450 km and a maximum fuel capacity of 216,840 L. We can calculate the fuel economy from this: 16L/km or 1600 L per 100 km. The number of passengers is ~500, so each passenger uses 3.2L per 100 km when the plane is full. This is similar to the fuel economy of a car!

Energy for cruising The rest of the fuel (~210,000L) is used to maintain “terminal” speed against air drag. Let’s estimate the drag force: A 747 has a fuel capacity of 216,840 L and a max. range of 13450km. So 210,000 L are used to counter air drag. W = F d, so F = 147 kN. (Engines have max thrust of 4 x 282 kN). It is less than the air drag on the ground (see Q4). Flying at a high altitude reduces the air drag because of a lower air density !! That’s why planes fly relatively high although further going high results in a lower upward lifting force.

Q4 Estimate of air drag of Boeing jets (speed about 915km/hr; cross-sectional area about 8mX3m) 150kN; 360kN; 3) 800kN; 4) 60kN.

Summary Use the work-energy relations to understand/ estimate the work done by thrust force for cruising or acceleration; 2) Estimate fuel economy of a car /air plane; 3) Understand the advantage of flying high.