http://www.hiper-laser.org/
Chris Edwards, S.T.F.C. Rutherford Appleton Laboratory (GB)
Cars
Cars
Want to know the energy in car fuel? Look at the label
on a pack of butter or margarine. The calorific value is
3000 kJ per 100 g, or about 8 kWh per kg.
A typical car-driver uses
about 40 kWh per day.
How British people travel
according to the 2001 census.
to
work,
1. Energy Lost During
Acceleration and Deceleration
1. Energy Lost During
Acceleration and Deceleration
2. Energy Lost Due To Air Resistance
A car moving at speed v creates behind it a tube of
swirling air; the cross-sectional area of the tube is similar
to the frontal area of the car, and the speed at which air in
the tube swirls is roughly v.
Energy dissipation is dominated by kinetic-energy-being dumped-into-the-brakes if the mass of
the car is bigger than the mass of the tube of air from one stop sign to the next; and energy
dissipation is dominated by making-air-swirl if the mass of the car is smaller.
d* : The special distance d. between stop signs, below which the dissipation is brakingdominated and above which it is air-swirling dominated (also known as drag-dominated).
4. Energy Lost To Heat
3. Energy Lost To Roling Resistance
The standard model of rolling resistance asserts that the force of rolling resistance is
simply proportional to the weight of the vehicle, independent of the speed. The constant of
proportionality is called the coefficient of rolling resistance, Crr.
The speed at which a car’s rolling resistance is equal to
air resistance is given by:
Optimized for 60 km/h
Most cars’ engines have an optimum revolution
rate, and the choice of gears of the car
determines a range of speeds at which the
optimum engine efficiency can be delivered.
Planes
100 x 12000 kWh /28400 = 42 kWh / 100 km
Planes
The total power required by the plane is the sum of the
power required to create lift (Plift) and the power
required to overcome ordinary drag.
Conservation of Momentum
http://www.youtube.com/watch?v=7xVjY6vakUE
The total power required by the plane is the sum of the
power required to create lift (Plift) and the power
required to overcome ordinary drag.
Let’s make a cartoon of the lift force on a plane moving at speed v. In a time t the plane
moves a distance vt and leaves behind it a sausage of downward-moving air. We’ll call the
cross-sectional area of this sausage As. This sausage’s diameter is roughly equal to the
wingspan w of the plane.
If the whole sausage is moving down with speed u:
Thrust (kN)
Speed (m/s)
This graph shows our cartoon’s estimate of the thrust required, in kilonewtons, for a Boeing
747 of mass 319 t, wingspan 64.4 m, drag coefficient 0.03, and frontal area 180m2,
travelling in air of density = 0.41 kg/m3 (the density at a height of 10 km), as a function of
its speed v in m/s. Our model has an optimal speed voptimal = 220 m/s (540 mph).
Optimal speed: 869 km/h
Drag-to-lift ratio
Freight
Some exercises:
What is the gas content of Earth’s atmosphere? What is the concentration of CO2?
Some exercises:
What is the gas content of Earth’s atmosphere? What is the concentration of CO2?
78 % N2 , 21% O2 , 0.03% CO2
Some exercises:
Why do we care about the CO2 concentration?
Some exercises:
Why do we care about the CO2 concentration?
Global warming.
Some exercises:
A 40W lightbulb is kept switched during one full day. How many kWh does this
correspond to?
Some exercises:
A 40W lightbulb is kept switched during one full day. How many kWh does this
correspond to?
40W x 24h = 960 Wh ~ 1 kWh
Some exercises:
Estimate the daily energy consumption of a person due to nutrition?
(Approximately 3000 kCal energy)
1kCal = 4186.8 J
Some exercises:
Estimate the daily energy consumption of a person due to nutrition?
(Approximately 3000 kCal energy)
1kCal = 4186.8 J
3.5 kWh
Some exercises:
Estimate the energy usage per a car driver using the relation below:
Some exercises:
Estimate the energy usage per a car driver using the relation below:
Some exercises:
Energy consumption of a car is given by the relation below. What should we do in
order to consume less energy during in-city driving or highway driving?
Some exercises:
Energy per distance for an airplane is given by the relation below. Interprete the
components of this equation. Sketch the ernergy per distance as a function of v.
Interprete your sketch.