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BASIC

GYROSCOPES

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An aircraft flying at 240 Km/Hr.Negotiates towards left and

completes aquarter of circle of 60m radius. Themass of rotary engine and propellerofplane amounts to 450 Kg. with aradiusof gyration of 320 mm. The enginespeedis 2000 r.p.m. clockwise. Whenviewedfrom the rear. Determine gyroscopic

couple on aircraft and state its effect.In what way is the effect changedwhenI)The aircraft turns towards rightII)The aircraft rotates clockwise whenviewed from the front (nose end) andaircraft turns toa) left andb) right

A small boat speeding at 30 Km/Hour takes

a turn towards left (Port side), into acircular path of 200 meters radius A steamturbine is fitted to the vessel such that theaxis of the rotating shaft is parallel to thelength of boat. The radius of gyration of therevolving masses revolving at 3000 rpm is40 cm. and their mass is 1500 Kg. Therevolving mass i.e. rotor of turbine issupported on bearing 4 mtrs apart. Thedirection of turbine rotor looking from thestern of the vessel is clockwise. Determine

the gyroscopic torque transmitted by thehull of the vessel and the manner in whichthis couple affects the balance of thevessel. Determine net reaction at thebearings(both forward and rear) and thedirection of reaction forces. The center ofgravity of rotor may be assumed at midspanof the bearing.(C = 3141.5 N-m, Rw = 7357.5 N RC = 785NRFB = 8142.87 N, RBB =6572.7 N )

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The heavy rotating masses i.e. Theturbine rotor of sea vessel rotates at1500 rpm, clockwise looking from theaft, its mass being 750 Kg. The vesselpitches with an angular velocity of 1rad/sec. Determine the gyroscopictorque transmitted to hull when the

bow is rising if radius of gyration of therotor is 25 cms. The rotating mass ofturbine is supported on the bearings 2.5mts. apart. Determine the net reactionon the bearings(both forward and rear)and the direction of reaction forces.The center of gravity may be assumedat mid-span of the bearings.(C = 7363 N-m, Rw = 3678.75 NRC = 2945.2N RFB = RBB =4712 .4733 NRFB(51.310) RBB(128.690)(FB=Forward

Bearing RB=Rear Bearing)

A cargo turbine rotor of a ship meant for drivingcargo pump has a mass of 400 kg. and has aradius of gyration of 350 mm. It rotates at aspeed of 10,000 rpm clockwise as seen from tofindi)The magnitude and direction of the reactivegyroscopic toque when ship steers to left in a

curve of 70 m radius at a speed of 17 knotsii)The magnitude and direction of the reactivegyroscopic toque when the ship pitches withSHM ,8 degree above and 8 degrees below themean position in time period of 25 sec.iii) The magnitude and direction of the reactivegyroscopic toque when the ship rolls with SHMdegrees left and 7 degrees right about verticalaxis in time period of 40 sec.

Each of the two paddle wheels of a steamerboat has a mass of 1800 Kgs and a radius ofgyration of 1.4 m. The paddles are rotating atspeed of 100 rpm in clockwise direction asseen from starboard side.Findi)The magnitude and direction of ReactiveGyroscopic torque acting when the boat turnsto left in a circle of 170 m radius at 25 km/Hr.ii)The magnitude and direction of ReactiveGyroscopic torque when the boat pitches withSHM ,9 degrees above and 9 degrees below

themean position in time period of 30 secondsiii)The magnitude and direction of ReactiveGyroscopic torque when when the boat rollswith SHM,8 degrees to left and 8 degrees toright about vertical axis in time period of 38sec.

A rear engine car is taking a left turn at

50kmph around a track o 120 m radius.Each wheel has a diameter of 500 mm andmoment of inertia of 1.5 Kg-m2 .Therotating parts of the engine have moment ofinertia of 0.8 Kg-m2 .The engine axis isperpendicular to the front and rear axlesand the engine rotates in clockwise directionviewed from the rear .The gear ratiobetween the engine and the rear axle is 4 : 1.The car has mass of 1500 kg with its centreof gravity 450 mm above the ground andthe centre of two axles. The wheel base is1.8 m and the width o the track is 1.5m.

Check the car for the stability .Findreactions at all the road wheels;accountingfor centrifugal forces, gravitational forceand gyroscopic effect.Reactions due to Front wheel Rear wheelInner Outer InnerOuterGravitational force 3678.75 3678.75 3678.75 3678.7Centrifugal force 361.69 361.69 361.69 361.69R.G.C. Wheels 12.86 12.86 12.86 12.86R.C.G. Engine 5.716 5.716 5.716 5.716Total 3298.484 3298.484 3298.484 3298.484

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A motorcyclist travels at 140 km/hr.

round a curve of 120 m radius .Thecycle

and rider have a mass of 150 kg. andtheir C.G. Is 0.7 m above ground level,

when the machine is vertical . Eachwheel is 0.6 m diameter and mass

moment of inertia about its axis ofrotation is 1.5 kg/m2 .The engine hasrotating parts whose moment of inertia

about their axis of rotation is 0.25kg/m2

and if it rotates at 5 times the wheelspeed in the same direction ,find i) The

angle of banking so that there will beno

tendency of side slip and ii)the angle of

inclination of the cycle and rider to thevertical.

( 55.54)