1. (25 points) An electric bicycle is being designed to

Question

1. (25 points) An electric bicycle is being designed to travel at 13 mph for 45 miles. We estimate the total
weight of the bicycle and rider, the rolling resistance coefficient for the tires, the frontal area, and the
drag coefficient for the bicycle. From these estimates we find that the total power required for the
bicycle is given by the equation below:
Total Power = (6.03 V + .027 V² + .048 V³) Watts
(Where the speed V is in mph)
a. If the rider uses only electric power, how much battery capacity is required to travel at 13 mph for 45
miles? (express your answer in watt-hrs) Assume that the electric motor and drive is 85% efficient in
converting the energy in the battery to mechanical energy.
b. Assume lithium-ion batteries provide 42 watt-hrs of energy storage per pound of battery, and the cost is
$12.00 per pound. Lead-acid batteries provide 21 wat-hrs of energy storage per pound, and the cost is
$2.00 per pound. (1) Calculate the weight and cost of using lithium-ion batteries. (2) Calculate the
weight and cost of using lead-acid batteries. (3) If you were going to ride this bicycle and have to pay for
it, which type of battery system would you choose?/nc. If the rider adds 60 watts power pedaling in addition to energy in the battery, how far can be traveled at
13 mph before the battery is depleted? Assume the chain drive for the bicycle is 100% efficient.
2. (25 points) You are designing a flat bed electric utility vehicle to be used in a manufacturing plant. The
vehicle will have space for a driver and one passenger and is capable of hauling up to 600 lb payload on the
bed. The maximum total weight for the vehicle is 2000 lb. The rolling coefficient for the tires is 0.018 and
the aerodynamic drag is negligible for this vehicle. The electric motor is 85% efficient and the drive system
connecting the motor to the wheels is 92% efficient. In making deliveries between two of the buildings the
vehicle will need to be able to climb a 6% grade at a minimum speed of 5 mph.
Parameter Summary:
Total weight 2000 pounds, Crr = 0.018
Aerodynamic drag is negligible.
Maximum grade is 6%.
Electric motor is 85% efficient.
Drive system is 92% efficient.
a. Calculate the total power the batteries must provide to
the electric motor to push the vehicle along on level
ground at 8 mph. Provide your answer in watts./nb. We would like to be able to use the vehicle all day without charging it. Assume that the vehicle will be
operating 50% of the time during a 10 hour shift, and the average power draw when operating is equal to
moving the vehicle along on level ground at 8 mph. Calculate the minimum energy storage required in the
batteries. Provide your answer in watt-hrs. At 48 watt-hr/lb for lithium-iron phosphate batteries, what is
the weight of the battery pack? Provide your answer in lb.
c. Calculate the power the electric motor must provide to push the vehicle (fully loaded) up a 6% grade at 5
mph. Provide your answer in watts.
3. (25 points) A small hybrid car has a total weight of 3300 lbs. The rolling resistance coefficient for the tires
is 0.009, the frontal area is 1.47 square meters and the drag coefficient is 0.29. The transmission and drive
system is 91% efficient in transmitting the engine power to the wheels. The fuel economy of the car is 62
mpg when driving on the highway at 70 mph.
1. Calculate the average power the engine must provide to push the car along at 70 mph. Assume level
ground and constant speed for this calculation. Express your answer in watts./n2. Assuming the car gets 62 mpg at 70 mph, calculate the fuel consumption in gallons per hour (gph).
3. Assuming that the vehicle burns the 10% ethanol blend gasoline which has 121,000 BTU per gallon,
calculate the fuel consumption (or fuel power) in watts. (watt = 3.412 BTU/hr)
4. Using the calculations above, calculate the average thermal efficiency of the engine when cruising on
the highway at 70 mph./n4. (25 points) Assume a 230 ton engine is pulling 25 cars that weigh 110 tons each at 58 mph for 1200
miles. The average rolling resistance coefficient is 0.005 for the train. The diesel locomotive is 33% efficient
in converting the energy in the diesel fuel into useful energy to power the train. Assume 138,700
BTU/gallon energy density for the fuel. To estimate aerodynamic drag, assume that the engine and each car
adds a drag area of A = 6 m² with a drag coefficient of Cd = 0.50. (hp = 2545 BTU/hr)
a. Calculate Total Weight of the train. Express your answer in
pounds. (ton 2000 lb)
CSX
b. Calculate the rolling resistance power required. Express your answer in hp.
c. Calculate the aerodynamic power required. Express your answer in hp.
d. Calculate the fuel consumption of the train traveling on level ground. Express your answer in gallons per
hour (gph). (Assume the fuel has 138,700 BTU/gallon)/ne. Calculate the time required for the 1200 mile trip (in hours) and the amount of fuel consumed (in
gallons).
5. (25 points) A jet airplane cruises at 520 mph. The mass of the jet airplane is 71,000 kg. The glide ratio
for the jet when traveling at cruising speed is 18.0. The density of the fuel is 2.88 kg per gallon. Assume
that the jet engines have a thermal efficiency of 35%, and that the engines use 90 kg of air for each kg of
fuel. The energy density of the fuel is 46.6 MJ/kg.
a. Estimate the drag force on the jet when cruising.
b. Calculate the velocity of the gasses exiting the jet engine, relative to the aircraft (Ve).
c. Calculate the required mass flow rate of fuel to the engines to generate enough thrust to equal the drag
force.
d. Assuming that the aircraft is carrying 150 passengers, calculate the passenger miles per gallon. Assume
the density of the fuel is 3.0 kg/gallon./n6. (25 points) According to the Department of Energy, the USA uses approximately 37.7 Quads of primary
energy in producing electricity each year, and produces 13.3 Quads of electricity. The mix of power plants
produces a total of 1584 million metric tons of carbon dioxide each year. (Quad = 1015 BTU) (KWH = 3412
BTU) (metric ton is 1000 kg)
a. Calculate the number of grams of carbon dioxide produced for each KWH of electricity produced.
b. The Nissan Ariya Kona has a range of 216 miles with a 91 KWH battery system. If the cars are sold
throughout the USA, then on average the electricity used to power the car will have the carbon footprint
calculated in (a) above. Using that number, what is the carbon footprint of the car in grams of carbon
dioxide per mile traveled?/n7. (25 points) We are using a fuel that has an average chemical composition of C6H12 and which has an
energy density of 47 MJ/kg. Assume the atomic mass is 12 for Carbon, 1 for Hydrogen and 16 for Oxygen.
(BTU = 1055 J)
a. Draw the C5H10 molecule below. (There are many correct possibilities, choose one of them.)
b. Write the chemistry formula for complete combustion of the fuel.
c. Calculate the mass of carbon dioxide generated by burning one kg of the fuel. Express your answer in
kg.

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