Answer :
The range for the converted electric Cessna 172, at maximum gross weight takeoff, is approximately 454.05 watt hours per kilogram.
Step 1: Calculate the maximum takeoff weight.
The maximum takeoff weight is the sum of the empty weight and the useful load weight. In this case, it is:
Maximum takeoff weight = Empty weight + Useful load weight
Maximum takeoff weight = 668 kg + 377 kg
Maximum takeoff weight = 1045 kg
Step 2: Calculate the available energy from the batteries.
The available energy is the charge density of the batteries multiplied by the battery weight. In this case, it is:
Available energy = Charge density of batteries x Battery weight
Available energy = 180 watt hour/kg x 220 kg
Available energy = 39600 watt hours
Step 3: Calculate the propulsive energy.
The propulsive energy is the available energy multiplied by the propulsive efficiency. In this case, it is:
Propulsive energy = Available energy x Propulsive efficiency
Propulsive energy = 39600 watt hours x 0.8
Propulsive energy = 31680 watt hours
Step 4: Calculate the range.
The range is the propulsive energy divided by the power required per unit distance (Preq). In this case, the power required per unit distance can be calculated using the lift-to-drag ratio (L/D). Assuming a constant velocity, the power required per unit distance is proportional to the weight of the aircraft divided by the lift-to-drag ratio.
Therefore:
Range = Propulsive energy / (Weight / L/D)
Range = 31680 watt hours / (1045 kg / 15)
Range = 31680 watt hours / 69.67 kg
Range ≈ 454.05 watt hours/kg
The range for a maximum gross weight takeoff of the converted electric Cessna 172 is approximately 454.05 watt hours per kilogram.
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