Range Analysis
Mission Summary
The max range was calculated by assuming that the aircraft would be flying with only one crew weighed at 90kg (198.4lbs). In this analysis, passengers were added one by one followed by their cargo. It was also assumed that the aircraft would have enough volume to store additional fuel weight for every passenger and cargo removed. The flight plan was also similar to the previous analysis with the main cruise section being affected to calculate the range. It was also assumed that the weight empty ratio would stay constant through the various payload weights.
Mission Profile
Figure 1, Flight profile for the analysis
The flight profile as seen in Figure 1 is identical to the flight profile used in the previous analysis. However only section 3 is affected in this analysis as section 3 defines the normal operating range.
Max Payload Range Calculations Figure 2, Calculation derivation for the range vs payload analysis
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Max Payload Range NotesThis calculation was done using Excel and utilized the formula set up seen in Figure 2. In the calculation, the SFC from the initial analysis was used and stayed constant despite the differing payload combination. The speed of the cruise and loiter was also assumed to be the same along with the takeoff and landing fuel consumption. The excel calculation resulted in Table 1 below with the corresponding plot Figure 3. Table 1, Calculation table for range vs payload. Figure 3, Range vs. payload plot |
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Results
The maximum possible range assuming constant SFC, empty weight ratio, the single crew at 90kg (198lbm) with no cargo, and all other parameters other than payload is 568 nmi or 1051.94 km. This value was also calculated assuming that for each mass lost in payload, the fuel of equivalent weight was added in turn. As seen in Figure 3, the relation of the range and payload is relatively linear where heavier payload results in less range. the range effectiveness of the aircraft seems to decrease significantly to a point where it may not be worthwhile to fly after allowing the aircraft to be boarded with 6 passengers and 20kg of cargo per passengers. Above this payload, it may be more effective to utilize conventional air taxis for this purpose since they can have a better range with the same amount of payload.
Electric Range Analysis
It was determined that the aircraft's MTOW would be determined to be 8767 lbm with a fuel weight fraction of 0.2846. This fuel weight fraction roughly translates to 2495 lb (1132 kg) of jet A fuel. This weight can be replaced with batteries and depending on the chosen motor, more batteries can be fitted in place of the proposed turbine engine's weight. For the engine sizing, using a value from Raymer for a tiltrotor aircraft of 4lb/hp[1], the aircraft would require 2191.88 hp (1634.5 kW) to perform vertical take-off. The horsepower of the engine and motor, in reality, would not be the most important parameter for aircraft performance. The aircraft's performance would depend on the amount of torque and propeller used. However, in this assumption, the horsepower rating was assumed to be the center of the analysis.
Currently, MagniX has produced aviation-certified electric motors. The most powerful motor produced by MagniX was the Magni500 which each produces 750 hp[2]. These engines each weigh roughly 300 lbm each and the aircraft would require four of these engines to meet the power loading requirement. The total power produced with these engines is roughly 2500 hp which is 100hp more than the initially planned PT6 turbine engine. The electric motor would have a total The two turbine engines were estimated to each weigh 572 lbs each which amounts to roughly 1150 lbm[3]. However, with the amount of power required, a robust and heavy writing system is required. This wiring system for the four engines can amount to a considerable weight.
Before these range analyses can be performed, the estimated power requirement of the aircraft must first be calculated. The cruise power requirement can roughly be calculated using the following equation:
In this equation, ηp was assumed to be 80%, and using the estimated L/D of 11.57. The aircraft weight was determined to be 8767 lbm (3976.6 kg) and velocity was assumed to be at cruise velocity of 277.8 km/hr (77.17 m/s). This analysis resulted in the power requirement of 325.3 kW. The motor's efficiency was described as 93% by the manufacturer which meant that it would be safe to assume the system efficiency to the propeller shaft ηb2s would be 90% [2]. The cruise run-time endurance in hours can then be calculated from the following equation from Raymer Equation 20.1 [1].
The battery chosen for this aircraft analysis was Lithium-Sulfur which was assumed to have 400 Wh/kg of specific energy. The chosen battery is considerably modern and is on the top end in terms of energy density [1]. As stated earlier, the battery's weight was assumed to replace the fuel weight which is equal to 1132 kg. Evaluating the equation results in cruise run-time endurance of 1.25 hours which is equivalent to roughly 75 minutes of cruise. Assuming cruise velocity of 277.8km/h, the aircraft would only be able to travel for 348 km which is within the required 348km range. This analysis neglects the power required for take-off and climb which would be significant and lower the range below the initially specified range.
Similarly, assuming that the aircraft requires 100% power which totals 2500hp, the vertical take-off endurance can be evaluated. This analysis yields in vertical take-off and hovers endurance of .2186 hours which is equivalent to 13 minutes of vertical acceleration and hover. This shows that it would not be feasible for the aircraft to take off vertically and have enough battery power left to travel to its destination.
However, the aircraft may be feasible for conventional take-off and landing albeit at a lower range. This can be roughly estimated by normalizing the power usages between vertical hover or take-off and the cruise. For the category of the aircraft, it can be assumed that the aircraft would be at 100% power for 10% of the travel time conservatively [4]. Breaking this down furthermore, the aircraft would be estimated to use 5% of its power to taxi and be at full power for a minute for taking off. The analysis can be seen in Figure 1 below.
Figure 1, Electric range analysis table.
This analysis was performed as follows:
- Taxiing was assumed to use 2% of the battery
- Take off was assumed to use 100% power for 1 minute which is equivalent to 7.62% of the maximum power endurance.
- The climb was assumed to utilize 10% of the battery as it was assumed that 10% of the travel time would be used to climb at 100% power.
- The descent was assumed to use 1% of the total fuel in case of loitering requirement.
- Landing and Taxiing at the destination were assumed to use 2% of the fuel.
- Finally, the remaining battery was assumed to be used for the cruise.
This analysis shows that it can be possible for the aircraft to meet the requirement. However, this can only be possible when the aircraft is limited to conventional take-off and landing. The aircraft would have a maximum range of 300km without any diversion range.
Sensitivity Study
The sensitivity study was approached by analyzing one variable at a time while keeping the others constant. This approach is very similar to an economics risk analysis and Excell was highly utilized for this analysis. The parameters analyzed in this analysis include Range, Empty weight fraction, L/D, SFC, and payload.
Composite Plot
Excel was heavily used to perform the sensitivity analysis. This calculation can be seen in Figure 1 as an example where the payload effect is analyzed in that sample.
Figure 1, Calculation table for the sensitivity analysis.
After performing the analysis seen in Figure 1 for each of the parameters, The effect of each parameter was normalized such that they can be compared relative to each other. This resulted in the sensitivity analysis plot seen in Figure 2. The table containing the data and the linear slope of each figure can be seen in Table 1.
Figure 2, The sensitivity analysis plot
Table 1, Table of results of the analysis.
Discussion of the Study
Range and SFC played a little effect on the take-off weight relative to the other four variables. This may because of the high energy density of the aircraft fuel being used in this application. The higher energy density of the aircraft allows for the aircraft to travel much further with little weight change caused by the added fuel. The empty weight ratio, however, was the most sensitive factor that affects the take-off weight. This is is expected as at least half of the aircraft's weight is the empty weight. The empty weight estimation method also played a big role as to why empty weight fractions play a big role in the design. The payload is the second most important factor in the maximum take-off weight since it is a major fraction of the aircraft's takeoff weight. Lastly, the third factor that produces a high impact on the take-off weight is the L/D ratio. The lift to drag ratio determines how effective the aircraft is and simultaneously affects both the range and SFC.
References
[1] D. Raymer, Aircraft Design: A Conceptual Approach, Sixth Edition. Washington, DC: American Institute of Aeronautics and Astronautics, Inc., 2018.
[2] “Products | MagniX.” https://www.magnix.aero/products
[3] European Union Aviation Safety Agency, “PT6A-67 Series Engine TYPE-CERTIFICATE DATA SHEET,” 2019.
[4] F. “Sandy” MacDonald, From The Ground Up. Ottawa: Aviation Publishers Co. Ltd., 2011.