Sizing: Mission Analysis
Mission Summary
The aircraft's mission is to be able to have a 300km (162nm) range while also being able to follow the IFR regulations provided in CAR 602.88. Following the propeller-driven airplane regulation, the aircraft should carry enough fuel for the range, two approach attempts, fuel to travel to an alternate aerodrome, land, and have enough reserve fuel to fly for another 45 minutes [1].
Flight Profile
Figure 1, The flight profile diagram of the aircraft.
The aircraft's fuel fraction was calculated using the worst possible scenario to meet the IFR regulation. As seen in Figure 1 above, the flight of the aircraft was divided into ton separate sections that are described as follows:
- The aircraft vertically takes off from the origin in a city which assumed to use 5% of the available fuel.
- The aircraft climbs to a cruising altitude of around 1828.8m (6000 ft).
- The aircraft cruises at 277.8 km/h (150kn) for a range of 300km (162 nmi).
- Aircraft enters a descent and attempts a vertical landing at destination aerodrome using 5% of the available fuel.
- Aircraft immediately enters loiter due to unspecified emergency or delay.
- The aircraft attempts a second landing using 5% of the available fuel.
- Aircraft climbs to an altitude of 1219.2m (4000 ft) to travel to the alternate aerodrome.
- Aircraft cruises at 277.8 km/h (150kn) for a range of 30km (16.2 nmi) to the alternate aerodrome.
- Aircraft enters a 45 minute loiter.
- Aircraft descents and performs a conventional landing.
Utilizing the maximum range, the aircraft can travel from Seattle-Tacoma International Airport [SEA] and travel to Ucluelet Seaplane Base [CAN3] which is within the 300km range (162nm) and divert to Tofino/Long Beach [CYAZ]. The flight radius centered around SEA along with the described route can be seen in Figure 2.
Figure 2, Range and flight path of the aircraft [2].
Figure 3, Flight plan of the aircraft [3].
Fuel Ratio Calculation
It was assumed that the aircraft uses 5% of the available fuel for every vertical take-off and vertical landing. Otherwise, Raymer's value(s) was used for the conventional landing, conventional take-off, climb, and descent [3].
The Raymer values are described as follows:
- Conventional warm-up and take off: 0.970
- Climb: 0.985
- Conventional landing: 0.995
Raymer has described some equations to calculate the cruise and loiter section of the flight which can be seen in Equations 1 and 2 below.
For cruise:
For Loiter:
During the loiter value, the L/D value is multiplied by a factor of 0.866 to represent the effectiveness of the aircraft for the configuration and speed at which the aircraft is flying.
Where the range is described in feet, velocity in ft/s, endurance in seconds, and Specific Fuel Consumption (SFC) in lbm/lb/s or 1/s. Assuming that the aircraft utilizes two separate turboprops, the propeller-specific fuel consumption (Cbhp) was assumed to be 0.5 per engine which was found in Raymer Table 3.4 [3]. However, since SFC is required, the value from table 3.4 must be converted using Equation 3 below.
Where V is the velocity in ft/s and ηp was assumed to be .8 as described in Reymer [3].
Using the equations above, the velocity of 277.8 km/h (150kn), and L/D of 11.568, the SFC was found to be as follows:
| 1x SFC Loiter @ 150 kn: | 7.99151E-05 | |||||
| 1x SFC Cruise @ 150 kn: | 9.58981E-05 | |||||
Once these values were calculated, the weight fractions for each section can then be calculated. The calculations were done using excel and the final values can be seen in Table 1. Finally, the wf/w0 can be calculated using Equation 4 seen down below.
The value of wf/w0 for the concept was calculated to be 0.283618373.
Table 1, Table of the fuel fraction wi/wi-1for each section.
Empty Weight Ratio Vs. Max Takeoff Weight Plot
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Figure 4, Plot of the Empty weight ratio vs take-off weight. |
Table 2, Aircraft used for research, see Appendix A for details. |
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The weight ratio plot was done utilizing 25 separate aircraft research data. The research data consists of aircraft specifications that are within the aircraft size, configuration, and mission. This limited the research to mostly twin-turboprop aircraft, twin-engined flying boats, and rugged amphibious bush-planes.
Iterative Max Takeoff Weight Calculation
The iterative calculation was done using the take-off weight equation provided in Reymer (Equation 3.4) which can be seen below.
The iterative calculation utilized the empty weight ratio s. max take-off plot equation. This was done completely using excel and resulted in Table 3 below.
Table 3, Iterative result.
The payload weight of 1212.54 lbs was used since the requirement had described that the aircraft must be capable of carrying 4 passengers at 90kg and luggage of 20kg each and a crew member weighed at 90k and cargo of 20kg.
The iterative calculation resulted in a maximum take-off weight of 8767.5 lbs which is equal to 3976.6 kg and an empty weight ratio of 0.577.
Results
The iteration for maximum take-off weight resulted in a maximum take-off weight of 8767.5 lbs and an empty weight fraction of .577. This value was achieved assuming that the cruise speed between the two cruise sections was the same as well as the speed at which the aircraft loiter is also the same. The range was assumed to be 300km (162nmi) for the main cruise portion while the divert range was assumed to be 30km (16.2nmi). This weight is somewhat heavy considering the size of the aircraft. As a comparison, a similarly sized G21 Widgeon considering it has 8000lbm MTOW[4]. However, for an amphibious VTOL design, this is can still be reasonable.
References
[1] “Canadian Aviation Regulations.” https://laws-lois.justice.gc.ca/eng/regulations/sor-96-433/page-91.html (accessed Feb. 09, 2021).
[2] “Draw a circle with a radius on a map.” https://www.mapdevelopers.com/draw-circle-tool.php?circles=%5B%5B300000%2C47.5413157%2C-122.341505%2C%22%23AAAAAA%22%2C%22%23000000%22%2C0.4%5D%2C%5B30000%2C48.9400106%2C-125.5349881%2C%22%23AAAAAA%22%2C%22%23000000%22%2C0.4%5D%5D (accessed Feb. 10, 2021).
[3] “SkyVector: Flight Planning / Aeronautical Charts.” https://skyvector.com/?ll=48.95,-125.55&chart=301&zoom=3 (accessed Feb. 10, 2021).
[4] J. W. R. Taylor, F. R. S. Hisf, and A. F. R. S. Ae, Jane’s All The World’s Aircraft 1974-75. Jane’s Information Group;, 1975.