Route planning in real time for short-range aircraft with a constant-volume-combustor-geared turbofan to minimize operating costs by particle swarm optimization

Figures & data

Figure 1. Block diagram of the route planning algorithm.

Figure 2. Social behavior of the PSO algorithm (Góez, 2016).

Figure 3. Cost function for route evaluation (Góez, 2016).

Table 1. Validation results

Parameter	Units	PMDF	PD
SFCsls	lb/lb/hr	0.317	−
SFCcr	lb/lb/hr	0.586	0.600^1
FNsls	lb	27,000	27,000 ^*
FNcr	lb	4,288	−
Engine weight	lb	5,248	5,250 ^*
Engine length	in	108.7	102.4 ^*
Fan diameter	in	69.4	68.3 ^*
Design range	nm	2,617	2,600 ^†
Block fuel	lb	34,774	−
Block time	hrs	6.08	−
MTOW	lb	172,483	162,920 ^‡
ZFW	lb	135,878	134,500 ^‡
Climb time to FL350	min.	19.5	−
Climb distance	nm	127.9	−
Climb fuel	lb	3,413	−
Descent time	min.	22.4	−
Descent distance	nm	109.2	−
Descent fuel	lb	570	−
Flyover noise	EPNdB	82	88 ^*
Sideline noise	EPNdB	93.6	94.4 ^*
Combined noise	EPNdB	175.6	182.4 ^*
LTO EINOx	g/kN	30.8	29.57 ^§
Total RF	W/m^2	1.27E-05	−
Price CFM56	USD	6.98	6.95 ^**
Price Airbus A320	USD	77.17	76.9 ^†
Total maintenance	$ct/ASM	2.02	2.01 ^††
Engine maintenance	$ct/ASM	0.68	0.67

^* Source: Jane’s Aero Engines 21st ed.

^† Source: Airbus.

^‡ Source: Jane’s All the World’s Aircraft ed. 2006–2007.

§ Source: ICAO Annex 16 volume2.

^** Source: CFM International.

^†† Source: Aircraft Commerce February/March 2007.

Figure 4. General description of the PMDF tool (Colmenares Quintero, 2009; Colmenares Quintero et al., 2010; Colmenares, Brink et al., 2009; Colmenares, Coutinho et al., 2009).

Table 2. Main performance parameters for GTF CVC

Parameter	Units	GTF-CVC
TET	°K	1,650
BPR	−	8.2
FPR	−	1.45
OPR	−	38.6
Mass flow	lb/s	926.9

Table 3. Simulation parameters

Description	Parameter PSO	Parameter CK
Population	40	40
Iterations	400	1000
Cruise speed	500 km/h	500 km/h
Roll	35	35
Turning ratio	2.33 g/sg	2.33 g/sg

Table 4. Coordinates of test routes

Route	Departure		Arrival
	Latitude N	Longitude	Latitude N	Longitude
1	5.7899	−75.6105	4.5334	−75.0242
2	4.5677	−75.2173	5.1307	−75.6588
3	5.7075	−74.6931	4.554	−75.2863
4	4.8218	−76.2382	4.9797	−74.5482
5	5.6389	−75.2311	4.4784	−75.3001

Table 5. PSO vs. CK

Route	Distance using PSO	Points per route using PSO	Distance using CK	Points per route using CK
1	205.54 ± 5.5	76.1 ± 1.9	262.7 ± 25.1	97.6 ± 10.0
2	80.00 ± 0.0	31 ± 0	95.7 ± 2.1	35.2 ± 1.3
3	165.41 ± 15.0	66.4 ± 5.2	498.6 ± 543.5	236.6 ± 303.2
4	197.61 ± 17.2	114 ± 7.3	447.5 ± 333.2	246.4 ± 171.0
5	114.16 ± 2.5	63 ± 8.3	194.0 ± 49.2	103.4 ± 21.3

Table 6. Flight parameters

Description	Parameter
Cruise speed	828 km/h (0.78 Mach)
Roll	35
Turn rate	2.33 °/s
Altitude	Varies for each test

Table 7. Optimization parameters of the algorithm

Description	PSO parameter
Population size	40
Visibility	20 km
Maximum number of PSO iterations	400

Figure 5. Route 1 analyzed in a contour map.

Figure 6. Route 2 analyzed in a contour map.

Table 8. Simulation results in terms of distance traveled

	Direct flight	Alternate route	Optimization algorithm
Route 1
Range[miles]	219.9	249.2	235.57
Flight time [h]	0.98	1.08	1.02
Fuel [lbs]	3,993.0	4,656.9	4,311.3
Route 2
Range [miles]	219.9	249.2	245.9
Flight time [h]	0.98	1.08	1.07
Fuel [lbs]	3,993.0	4,656.9	4,511.3

Table 9. Optimized route vs alternate route: route 1

30-year operating cost	Optimized route M$	Alternate route M$
Engine direct operating cost	121.7	123.14
Total direct operating cost	255.32	255.68
Total indirect operating cost	278.18	283.02
Noise fees	2.52	2.61
Emissions fees	1.72	2.06
Fuel cost	90.65	93.03
Total maintenance cost	75.92	74.34
Life cycle cost	578.64	582.76

Table 10. Optimized route vs alternate route: route 2

30-year operating cost	Optimized route M$	Alternate route M$
Engine direct operating cost	128.73	123.14
Total direct operating cost	259.53	255.68
Total indirect operating cost	267.28	283.02
Noise fees	2.33	2.61
Emissions fees	1.84	2.06
Fuel cost	99.26	93.03
Total maintenance cost	73.17	74.34
Life cycle cost	571.0	582.76

Góez, G. D. (2016). Planeamiento de Rutas en Vehículos Aéreos No Tripulados usando Algoritmos Bio-inspirados sobre Sistemas (MSc Thesis). Instituto Tecnologico Metropolitano, Medellin, Colombia.

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Colmenares Quintero, R. F. (2009). Techno-economic and environmental risk assessment of innovative propulsion systems for short-range civil aircraft ( PhD Thesis). Cranfield University, Cranfield, UK.

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Colmenares Quintero, R. F. , Brink, R. , Ogaji, S. , Pilidis, P. , Colmenares Quintero, J. C. , & Quintero, A. G. (2010). Application of the geared turbofan with constant volumecombustor on short-range aircraft: A feasibility study. Journal of Engineering for Gas Turbines and Power , 132 (6), 061702. doi:10.1115/1.4000135

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