Assignment No: 01 Name: Deepak Paul Tirkey Course code: AE4314 Student Number: 4590929 __________________________________________________________________________________ Question 1 Define and compare a helicopter to other existing designs Answer: My chosen helicopter is MBB Bo 105. Bo105 is a light utility, twin engine, multipurpose helicopter developed by MBB Germany in the early 1960’s. It features 4 bladed soft inplane hingeless main rotor system which makes it highly manoeuvrable. It can perform steep dives, rolls, loops, turnovers etc. It is used for reconnaissance and surveillance, Emergency medical services, and in armed version as a light attack platform. With over 1500 numbers of this helicopter build, it is serving in around 21 different countries. Some of its leading performance parameters and that of the other helicopters in the same class and similar role are listed in the table below.

Performance parameters

MBB Bo105

Eurocopter AS350

Bell 206

Bell 407

Bell 427

MD explorer

Crew 2 1 1 1 2 2

passengers 4 5 4 5 7 6

Empty weight 1276 kg 1174 kg 1057 kg 1210 Kg 1760 Kg 1531 Kg

Max. takeoff wt 2500 kg 2250 kg 1451 kg 2722 Kg 2970 Kg 3129 Kg

Useful load 1224 kg 1114 kg 971 kg 997 kg 1340kg 1417.5 kg

Power plant 2X 313 kW

1x 632 kW 1x 310kW derated

1x 606 kW 2x 529kW 2x 410 kW

Engine Model Allison 250-C20B

Turbomeca Arriel 2B

Allison 250-C30P

Allison 250-C47B

P & W PW207D

P & W PW206E

Takeoff Power TOP 313 kw 632 kW* 650 kW 650 kW 426 kW $ 482 kW

Max continuous Power MCP

298 kW 543 kW 501 kW 600 kW 426 kW 426 kW

Never Exceed speed 270 km/h 287 km/h 241 km/h 279 km/h 259 km/h 259 km/h

Maximum speed 242 km/h 260 km/h 222 km/h 260 km/h 259 km/h 250 km/h

Cruise speed 204 km/h 245 Km/h 219 km/h 246 Km/h 250 Km/h 244 Km/h

Range 575 km 662 km 693 km 598 km 730 km 1500 km

Endurance 2 hr 10min

4.1 hr 3.7 hr 4 hr 4 hr 3 hr 12min

Service ceiling 5180 m 4600 m 4115 m 5698 m 3048 m 5335 m

Hover ceiling (IGE) 3.7 km 3.5 km 4.8 km # 1.6 km 4.8 km 3.4 km

Hover ceiling (OGE) 2.4 km 2.9 km 1.9 km 1.6 km # 2.3 km 2.9 km

Rate of climb 8 m/s 8.5 m/s 6.9 m/s 4.1 m/s 10.16 m/s 5.1m/s

Table 1. Eurocopter AS350 is well known for its high altitude performance including landing on top of Mount Everest at 8848 meters in its stripped down version. It has carried out a number mountain rescue missions. It has very low levels of cabin noise. From among the helicopters compared in the table 1 , among other bell family copters, Bell 427 with twin Pratt and Whitney PW207D With much higher power output exceeds Bo105 in performance parameters except for its low service ceiling. MD explorer designed in the early 1990s by McDonnell Douglas features NOTAR anti torque system instead of the conventional tail rotor system which makes it far less noisy with increased safety level. With Pratt and Whitney PW206E twin engines it has highest range as well as increased MTOW. Its rate of climb is low. __________________________________________________________________________________ Source: 1. www.bellhelicopter.com 2. www.airliners.net 3. # www.westwindhelicopters.com/specs/

4. Wikipedia 5. airbushelicoptersinc.com 6. $ EASA type certificate data sheet 7. * Arriel 2Bx-2Cx data sheet

Assignment No: 01 Name: Deepak Paul Tirkey Course code: AE4314 Student Number: 4590929 __________________________________________________________________________________ Question 2 Moment of inertia calculations

Fig.01 MBB Bo105 Helicopter

For moment of inertia ( 𝐼𝑌𝑌) calculations the helicopter has been broken down into the following

segments: 1. Main rotor 2. Tail rotor 3. Fuel tank 4. Engine 5. Fuselage and 6. Tail boom as shown in

Fig.01.

For creating different coloured segments and dimensioning them, Inkscape (vector graphics) and

Gimp (Raster graphics) tools were used. Different geometrical objects like ellipsoid, rectangular

parallelepiped, cylinder etc were overlaid on the 3 view drawing of the helicopter using Inkscape.

Using the measure tool from Gimp, the dimensions of a segment were measured in pixels.

Scale: Horizontal 1 pixel ≡ 0.015 meter

Vertical 1 pixel ≡ 0.015 meter

Individual contributions of different segments towards the MoI 𝐼𝑌𝑌 are :

1. Main rotor contribution: main rotor is approximated by a disc. It is located vertically at a

distance d (102 pixel = 1.53 m). Polar Moment of inertia J = 1

2 m𝑅2=918 kg𝑚2 .

Radius R = 4.92 m. Using R and J , mass of the main rotor m = 75.85 kg.

Moment of inertia about disc plane (parallel to Y axis of helicopter) 𝐼𝑦 = 1

4 m𝑅2=459 kg𝑚2.

Using parallel Axis theorem 𝐼𝑌 = 𝐼𝑦 + m𝑑2 = 459 + 75.85 x 1.532 = 636.56 kg𝒎𝟐

2. Tail rotor contribution: tail rotor is approximated by a disc. It is located vertically at a

distance e (116 pixel = 1.74 m) and horizontally at distance l (395 pixel = 6.023 m). Polar

Moment of inertia J = 1

2 m𝑅2=0.94 kg𝑚2 . Radius R = 0.95 m. Using R and J , mass of the tail

rotor m = 2.08 kg.

Using parallel Axis theorem 𝐼𝑌 =𝐽 + m(𝑙2 + 𝑒2)=0.94 + 2.08 x (6.0232 + 1.742) = 82.7 kg𝒎𝟐

3. Fuel tank contribution: Fuel tank is approximated by a rectangular parallelepiped. It is

located vertically at h ( 46 pixel = 0.69 m) and horizontally at m (28 pixel =0.43 m).

Dimensions of the fuel tank are: length = 2.8 m (185 pixel) and width = 1.5 m (100 pixel).

Height (0.014m) of the fuel tank was approximated to give fuel volume capacity of 58 litres

Assignment No: 01 Name: Deepak Paul Tirkey Course code: AE4314 Student Number: 4590929 __________________________________________________________________________________

(fuel density = 8 kg /litre). MBB Bo105 helicopter has two fuel tanks, main and supply tank

and can carry a maximum of 464 kg of fuel . MoI of the fuel tank about its own principal axes

(parallel to Y axis of helicopter) 𝐼𝑦 =𝑚𝑎𝑠𝑠

12(𝑙𝑒𝑛𝑔𝑡ℎ2 + ℎ𝑒𝑖𝑔ℎ𝑡2) = 303 kg𝑚2.

Using parallel Axis theorem

𝐼𝑌 = 𝐼𝑦 + mass x (ℎ2 + 𝑚2) = 303 +464 x (0.692 + 0.432) = 608.5 kg𝒎𝟐

4. Engine : MBB Bo105 helicopter uses Alison 250 model engine in two quantity. Dry weight of

a single engine is 62 kg. it can be dimensionally approximated as a cylinder of length 1.029 m

and diameter 0.572 m . It is located vertically at f ( 55 pixel = 0.83 m) and horizontally at

j (26 pixel =0.43 m). MoI of a single engine about its own principal axes (parallel to Y axis of

helicopter) 𝐼𝑦 =𝑚𝑎𝑠𝑠

12(3 x 𝑟𝑎𝑑𝑖𝑢𝑠2 + 𝑙𝑒𝑛𝑔𝑡ℎ2) =

62

12(3 x 0.2862 + 1.0292) = 6.74 kg𝑚2.

For two engines 𝐼𝑦 = 2 x 6.74 = 13.48 kg𝑚2.

Using parallel Axis theorem

𝐼𝑌 = 𝐼𝑦 + 2 mass x (𝑓2 + 𝑗2) = 13.48 +2 x 62 x (0.832 + 0.432) = 117.72 kg𝒎𝟐

5. Fuselage: fuselage is approximated by an ellipsoid of the dimensions : 2a(282 pixel = 4.3 m)

Length along longitudinal direction; 2b (142 pixel = 2.13 m) height and 2c (120 pixel = 1.8 m)

along the width. Mass of the fuselage is approximated as 1500 kg . it is located horizontally

at a distance of m (28 pixel =0.43 m). MoI of the fuselage about its own principal axes

(parallel to Y axis of helicopter)

𝐼𝑦 =𝑚𝑎𝑠𝑠

5(𝑎2 + 𝑏2) =

1500

5(2.152 + 1.0652) = 1727 kg𝑚2

Using parallel Axis theorem

𝐼𝑌 = 𝐼𝑦 + mass x (𝑚2) = 1727 + 1500 x (0.432) = 2000.5 kg𝒎𝟐

6. Tail boom: Tail boom is approximated by a cylinder of length 3.6m (234 pixel) and dia 0.30m.

It weighs around 34 kg and is located vertically at g(35 pixel = 0.525 m) and horizontally at k

(206 pixel = 3.14m). MoI of the tail boom about its own principal axes (parallel to Y axis of

helicopter) ) 𝐼𝑦 =𝑚𝑎𝑠𝑠

12(3 x 𝑟𝑎𝑑𝑖𝑢𝑠2 + 𝑙𝑒𝑛𝑔𝑡ℎ2) =

34

12(3 x 0.152 + 3.62) = 36.8 kg𝑚2

Using parallel Axis theorem

𝐼𝑌 = 𝐼𝑦 + mass x (𝑔2 + 𝑘2) = 36.8 + 34 x (0. 5252 + 3.142) =381.4 kg𝒎𝟐.

Summary

Segment Mass (kg) 𝐼𝑌 (kg𝐦𝟐)

Main rotor 75.85 636.56

Tail rotor 2.08 82.7

Fuel tank 464 608.5

Engine 62 x 2 117.72

Fuselage 1500 2000.5

Tail boom 34 381.4

Total 2200 kg 3827 kg𝒎𝟐 Moment of inertia of the MBB Bo105 helicopter in the Y axis with an all up weight of

2200 kg is 𝐼𝑌𝑌 = 3827 kg𝒎𝟐

[Note: 𝐼𝑌𝑌 = 4973 kg𝑚2 for Ma = 2200 kg as per Padfield. Possible sources of error in my calculations

are : error in CG location, non inclusion of horizontal tail with end plates and vertical fin, measurement

error using image, assumed weight for fuselage and tail boom and assumed geometrical shapes.]

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Source: 1. Eurocopter Bo105 Tech defn. 2. www.thgmbh.com/bo105 3. wikipedia

4. Helicopter flight Dynamics – G Padfield 5. Inkscape.org 6. Gimp.org