Textbook of Engineering Drawing, Second Edition

_____ Geornetrical Contructions 4.41

2. Divide PO and SR into any number of (4) equal parts as 1, 2, 3 and 11 , 21 , 31 respectively
   starting from P on PQ and from S on SR. Join VI, V2 & V3. Also join VIr, V21, V3^1

3. Divide PO and OS into 4 equal parts as 11 ,2 1 ,3 1 and 1 \ ,2\ ,3^11 respectively starting from

P on PO and from S on SO.

4. From 1 I draw a line parallel to PQ to meet the line VI at PI' Similarly obtain the points P:
   and P .. ,

5. Also from 1\ ,2^11 ,3\ draw lines parallel to RS to meet the lines VII, V21, and V3^1 at P/,

P 2 I, and P3^1 respectively and draw a smooth parabola

Problem: A fountain jet discharges water from ground level at an inclination of 55° to the ground.
The jet travels a horizontal distance of 10m from the point of discharge and falls on the ground.
Trace the path of the jet.

Solution : (Fig.4.60)

Fig. 4.59

1. Taking the scale as 1: 100 draw PQ = 10 em. Jet discharges water at 55° to the ground. So,

at P and Q draw 55° lines to intersect at R. PQR is an isosceless triangle.

2. Bisect PQ at O. At 0, erect vertical to pass through R. Bisect OR at V, the vrtex.


3. Divide PR into any number of (say 8) equal parts as 1, 2, ... 7 starting from P on PR. Divide
   RQ into same number of (8) equal parts as 11 , 21 .... 71 starting from R on RQ.


4. Join 1,11 and also 7,7^1. Both will meet the vertical OR at a point. Join 2, 21 , and also 6, 61 ,.
   Both will meet the vertical OR at another point. Join 3,3^1 and also 5,5^1. Both will meet the
   vertical OR at a third point. Join 4,41 and it will meet the vertical OR at V.


5. Draw a smooth parabola through P, V, Q such that the curve is tangential to the lines 1 II,
   221, .... 771.
   Problem: Construct a conic when the distance of any point P between the focus and the directrix
   is constant and is equal to 50mm and its eccentricity is 3/2. Name the curve. Draw a tangent and
   a normal at any point on the curve.
   Solution: (Fig.4.61)


6. As the eccentricity is greater than 1; the curve is a hyperbola. Draw one directirx DD and

mark the focus F such that FA = 50 mm.

2. As the eccentricity is 3/2, divide FA into 3 + 2 = 5 equal parts. By difinition VF N A = 3/2 and
   hence locate the vertex V.