On average the mass of passenger luggage carried by an aircraft is 30 kg (including checked and carryon luggage). Assume a plane carries 200 passengers and always flies with a full load. The mass of...

On average the mass of passenger luggage carried by an aircraft is 30 kg (including checked and carryon luggage). Assume a plane carries 200 passengers and always flies with a full load. The mass of the aircraft and passengers (not including luggage) is 350000 kg. The plane flies at an altitude of 10 km and at a velocity of 200 m/s. Assuming a simple view of flight, the upward lift force must be equal to the downward force caused by gravity to keep the plane at a constant altitude (Figure on the left). For this aircraft, the ratio of the drag force to the lift force is 0.025 and is constant. For simplicity, assume the plane will fly 2000 km at a constant altitude (level flight), and plane and all of its components are isothermal.

1. The efficiency of the aircraft engine is 45%, which is defined as desired power output /required heat input. The cost of aircraft fuel is $0.86/liter. The energy content of the fuel is 43 MJ/kg. Density of the fuel is 0.8 kg/liter. At the end of the flight, there will be 10% of the initial mass of the fuel left in the airplane tank. Determine the mass and volume of the fuel, and the cost to complete this level (constant altitude) flight. Your approach should be based on an energy balance of the plane.HINTS:
   
   
   • Are there any energy (thermodynamic property of the system) changes in this process?
   
   
   • The mass of fuel during this flight will be changing and affecting the total mass of the plane which affects the drag force on the aircraft. Therefore, power needed for flight and fuel consumption rate will change during the flight.
   
   
   • One way of including the effect of the varying mass of the fuel is to use the differential form of the energy balance. In this case, one looks at an arbitrary position within the flight path (see figure on the right) and uses the small incremental energy interactions. There is no change in specific internal energy in this problem because we are assuming an isothermal process. The benefit of the differential form of the energy balance is that the parameters in the problem can be stated as a particular value at an arbitrary position (a time snapshot) within the flight. i.e. solving for a small incremental displacement δs and evaluating corresponding incremental work (δW), heat (δQ), and other small property changes (for example, dU if any). at a particular position (or time) during flight. This allows one to recast the energy balance into an expression that could be solved for the change in the mass of fuel over the flight distance. This usually involves integration or solving a differential equation over the entire travelled distance and simplifies the solution.
   
   
   • If one knows how the mass of the fuel changes over the flight distance one can complete the energy balance between the initial and final states.
   
   
   
   


2. It is being proposed that a design in which the aircraft is powered by electrical motors and batteries be investigated for its feasibility. The mass of the motors is expected to be the same as that of the engines. The energy storage and mass of the battery packs needed to perform the flight as described in the question need to be determined. Note that in this problem, the total mass of the batteries does not change during the flight. It is standard practice to discharge a battery to 20% to prolong battery life. Hence, we expect, the batteries will contain 20% of their energy capacity at the end of the flight. As a design starting point you should use the characteristics of the battery packs used in the current hybrid and electric vehicles (do some research to figure out what is available), for example the Toyota brands or Tesla. Determine the required battery mass for the energy required for the entire flight. Based on your calculations, is this a feasible design option?


3. Based on the battery specifications you selected in part B, determine the mass of batteries needed to supply the power to maintain the constant velocity and flight altitude in this problem. In this case, you will need to convert the energy balance from an energy statement to a power statement using the relationship between power and energy. Is the answer for this part the same as in part B? Would this option be feasible from a power perspective?


4. There are also technologies such as flow cells or flow batteries or fuel cells that are used to store chemical energy or hydrogen to produce electricity. Using a high-level literature search to determine the performance, energy density of these technologies and compared it that for batteries you have chosen in part B. Would these technologies be an alternative to batteries?