AEM 495 MEMO
Subject:
Aircraft Modification Sensor Package
TO:
Charles O’Neill
Date:
16 September 2014
CC:
Ned Covair
Dieter Corvallis
Memo:
AEM495-14-M03-RevA
From:
Malory McLemore
REF:
Aircraft Modification: Sensor Package
Ext:
Summary:
This memo addresses the attachment of the MX-25 sensor to the belly of the
Gulfstream G550 Aircraft. The sensor would add a drag count of approximately 4.39, a
1.6% increase in the drag count for the entire aircraft. I do not recommend the
placement of the antennas aft of the sensor due to the unstable vortices and turbulent
flow that can form behind a spherical shape at high velocities.
Discussion:
I.
MX-25 Drag Impact
The MX-25 sensor is spherical and attached to the belly of the aircraft with a cylindrical
mount. To estimate the drag polar, the sensor was modeled as a combination of a
sphere and a cylinder. The sensor is 25.7” in diameter and 30.2’ in height (Figure 1).
The drag coefficient for a sphere varies greatly with Reynolds number and Mach
number.
𝐶𝐷 = 𝐶𝐷 (𝑅𝑒, 𝑀)
A mathematic estimate for this relationship was published by R. Shankar Subramanian
of Clarkson University. It is given by,
𝐶𝐷 = 0.1𝑤 − 0.49 𝑓𝑜𝑟 4 ∗ 105 ≤ 𝑅𝑒 ≤ 106 ,
and
8 ∗ 104
𝐶𝐷 = 0.19 −
𝑓𝑜𝑟 106 < 𝑅𝑒,
𝑅𝑒
where,
𝑤 = log10 𝑅𝑒.
Figure 1: Sensor Configuration
The CD for a short cylinder does not vary as much with Mach number and Reynolds
number as a sphere does, so it was assumed to be
𝐶𝐷 = 0.85.
The maximum cruising altitude for the Gulfstream G550 aircraft is 51,000 ft. The entire
flight envelope for the aircraft is graphed in Figure 2. Drag counts were approximated at
an altitude of 51,000 feet, 45,000 feet, and 30,000 feet. The speed of sound, density,
and kinematic viscosity are compiled in Table 1.
Altitude
30,000
45,000
51,000
a [ft/sec]
992.93
966.53
966.53
ρ
[slugs/ft3]
8.91E-04
4.62E-04
3.47E-04
μ [lb*s/ft2]
3.11E-07
2.97E-07
2.97E-07
Table 1. Atmospheric Data
The Reynolds number was calculated by
𝑀
𝜌𝑎𝐷
𝑅𝑒 =
𝜇
Figure 2: G550 Flight Envelope
Where,
𝐷 = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑒𝑛𝑠𝑜𝑟 = 25.7 𝑖𝑛𝑐ℎ𝑒𝑠.
The size of the entire aircraft was considered in order to calculate accurate drag counts
for the sensor. An online analysis of the G550 calculates the drag coefficients based on
reference area at Mach 0.8 and an altitude of 45,000 feet,
𝐶𝐷𝑡𝑜𝑡𝑎𝑙 = 0.02771.
The reference area for this calculation was
𝐴𝑅𝑒𝑓 = 1137.00 𝑓𝑡 2
The Reynolds number, CD for the sphere, average CD, and the drag counts are
compiled in Table 2. The CD average is calculated by,
𝐶𝐷 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 = 𝐴𝑅𝑒𝑓 ∗
𝐶𝐷𝑆𝑝ℎ𝑒𝑟𝑒 + 𝐶𝐷 𝐶𝑦𝑙𝑖𝑛𝑑𝑒𝑟
2
The summary of the results requested by aerodynamics performance engineer, Ned
Corvair, concerning the sensor’s drag impact across the aircrafts flight envelope, are
given in Table 3. These results are reasonable considering that the entire aircraft would
have an approximate drag count of 277.1, and the sensor would add an average drag
count of 4.39. This is a 1.6% increase in the drag count for the entire aircraft.
H= 51000ft (Maximum Cruise Altitude)
Drag Counts
Locally Transonic?
4.1604
No
4.2825
No
4.3656
Yes
4.3916
Yes
4.4118
Yes
H= 45000ft
Mach
Drag Counts
Locally Transonic?
0.3
4.2151
No
0.5
4.3550
No
0.7
4.4174
Yes
0.8
4.4369
Yes
0.9
4.4521
Yes
H= 30000ft
Mach
Drag Counts
Locally Transonic?
0.3
4.3811
No
0.5
4.4581
No
0.7
4.4910
Yes
0.8
4.5013
Yes
0.9
4.5093
Yes
Mach
0.3
0.5
0.7
0.8
0.9
Table 2: Summary of Drag Counts
II.
Communications Antenna Placement
For the antenna placement problem, I recommend that the antennas be moved to
another location or that a non-spherical sensor be attached to reduce turbulent flow. I
agree with Dieter Corvallis’ concerns about the current placement of the sensor and the
effect on the aircraft’s communications antennas. The spherical shape of the sensor
causes unstable vortices to form on the belly of the plane in the location of the UHF
communications antenna and the proposed GPS antenna. A spherical shape causes a
pair of stable vortices to form on the downward side at a low velocity. As velocity
increases, these vortices become unstable and are alternately shed downstream of the
sensor towards the location of the antennas. As the velocity continues to increase, the
boundary layer transitions to turbulent flow with vortices of many different scales being
shed. These unstable vortices would compromise the stability of the sensor, possibly
causing them to snap off of the aircraft.
H= 51000 ft (Maximum Cruise Altitude)
w
CD (Sphere)
CD (Cylinder)
Mach
Velocity
Re
CD (Average)
Drag Counts
0.3
0.5
0.7
0.8
0.9
289.96
483.27
676.57
773.23
869.88
7.26E+05
1.21E+06
1.69E+06
1.93E+06
2.18E+06
5.86
6.08
6.23
6.29
6.34
0.0004160
0.0004283
0.0004366
0.0004392
0.0004412
4.1604
4.2825
4.3656
4.3916
4.4118
Mach
Velocity
Re
w
CD (Average)
Drag Counts
0.3
0.5
0.7
0.8
0.9
289.96
483.27
676.57
773.23
869.88
9.66E+05
1.61E+06
2.25E+06
2.58E+06
2.90E+06
5.99
6.21
6.35
6.41
6.46
0.85
0.85
0.85
0.85
0.85
0.0004215
0.0004355
0.0004417
0.0004437
0.0004452
4.2151
4.3550
4.4174
4.4369
4.4521
Mach
Velocity
Re
w
CD (Sphere)
CD (Cylinder)
CD (Average)
Drag Counts
0.3
0.5
297.88
496.47
1.83E+06
3.05E+06
6.26
6.48
0.14627
0.16376
0.85
0.85
0.0004381
0.0004458
4.3811
4.4581
0.7
0.8
0.9
695.05
794.35
893.64
4.27E+06
4.88E+06
5.49E+06
6.63
6.69
6.74
0.17126
0.17360
0.17542
0.85
0.85
0.85
0.0004491
0.0004501
0.0004509
4.4910
4.5013
4.5093
0.09607
0.85
0.12384
0.85
0.14275
0.85
0.14865
0.85
0.15325
0.85
H= 45000 ft
CD (Sphere)
CD (Cylinder)
0.10851
0.14032
0.15452
0.15895
0.16240
H=30000 ft
Table 3: Intermediate Calculations
References:
http://exploration.grc.nasa.gov/education/rocket/sized.html
http://web2.clarkson.edu/projects/subramanian/ch301/notes/dragsphere.pdf
http://en.wikipedia.org/wiki/Drag_coefficient
http://www.lissys.demon.co.uk/samp2/
Further Information
If further information is needed regarding the aircraft modification, contact Malory
McLemore at mamclemore1@crimson.ua.edu.