Principles of Orthographic Projections: First Angle vs. Third Angle Systems

---

1. Principles of Orthographic Projection

Orthographic projection is a parallel projection technique where the lines of sight (projectors) are mutually parallel and perpendicular to the plane of projection.

Reference Planes of Projection:

1. Vertical Plane (VP): Fixed vertical datum plane. The projection on VP is called the Front View (FV) or Elevation.
2. Horizontal Plane (HP): Fixed horizontal datum plane. The projection on HP is called the Top View (TV) or Plan.
3. Profile Plane (PP): Perpendicular to both HP and VP. The projection on PP is called the Side View (SV) or End View.
4. Reference Line ($XY$): The intersection line between HP and VP.

The Rotation Rule (Unfolding the Planes):

To represent a 3D object on a flat 2D sheet:

• The VP is kept stationary.
• The HP is rotated $90^\circ$ clockwise about the $XY$ axis until it lies flush in the plane of the VP.

       2nd Quadrant      |      1st Quadrant
   (Above HP, Behind VP) | (Above HP, In Front of VP)
                         |
  -----------------------+----------------------- HP
  Behind VP              |             In Front of VP
                         |
       3rd Quadrant      |      4th Quadrant
   (Below HP, Behind VP) | (Below HP, In Front of VP)
                         |
                         VP

---

2. Why Second and Fourth Quadrants are Not Used in Engineering Practice

• Second Quadrant: Both HP and VP views lie above the $XY$ line after clockwise rotation of HP. Top view and front view overlap, creating visual ambiguity.
• Fourth Quadrant: Both HP and VP views lie below the $XY$ line after clockwise rotation of HP. Views overlap and create complete confusion.
• Conclusion: Only First Angle and Third Angle projections yield completely separated, distinct views.

---

3. Comprehensive Comparison: First Angle vs. Third Angle Projection

Parameter / Feature	First Angle Projection (BIS / ISO Standard)	Third Angle Projection (ANSI / USA Standard)
Object Position	Object is placed in the $1^{\text{st}}$ Quadrant.
(Above HP, in front of VP).	Object is placed in the $3^{\text{rd}}$ Quadrant.
(Below HP, behind VP).
Spatial Sequence	Observer $\rightarrow$ Object $\rightarrow$ Plane.
(Object lies between observer and plane).	Observer $\rightarrow$ Plane $\rightarrow$ Object.
(Plane lies between observer and object; plane assumed transparent).
Front View (Elevation)	Placed ABOVE the reference line $XY$.	Placed BELOW the reference line $XY$.
Top View (Plan)	Placed BELOW the reference line $XY$.	Placed ABOVE the reference line $XY$.
Left-Hand Side View	Projected and placed on the RIGHT of the Front View.	Projected and placed on the LEFT of the Front View.
Right-Hand Side View	Projected and placed on the LEFT of the Front View.	Projected and placed on the RIGHT of the Front View.
Adopting Standards	Followed in India (BIS SP 46: 2003), UK, Europe, ISO.	Followed in USA, Canada, Japan.

---

4. Standard Projection Symbols (Frustum of a Cone)

To avoid ambiguity, every technical drawing must display the standard projection symbol inside the Title Block. The symbol is based on the two views of a truncated cone (frustum) of large diameter $D$, small diameter $d = D/2$, and length $L = D$.

A. First Angle Projection Symbol:

• The circular view lies on the right-hand side of the trapezoidal front view.

       +----+                  ( O )
      /      \                (     )
     +--------+                ( O )
    Trapezoid View          Concentric Circles
      (Front View)          (Left View placed on Right)

B. Third Angle Projection Symbol:

• The circular view lies on the left-hand side of the trapezoidal front view.

       ( O )                  +----+
      (     )                /      \
       ( O )                +--------+
 Concentric Circles       Trapezoid View
   (Left View on Left)      (Front View)

---

5. Summary of Key Exam Points

1. First Angle Rule of Thumb: Everything is opposite! (Top view below, Left view on right, Right view on left).
2. Third Angle Rule of Thumb: Natural view positions (Top view on top, Left view on left, Right view on right).
3. Notation Convention:
   • Real point in space: Capital letters ($A, B, C$).
   • Top View (Plan): Lowercase letters ($a, b, c$).
   • Front View (Elevation): Lowercase letters with primes ($a', b', c'$).
   • Side View (End View): Lowercase letters with double primes ($a'', b'', c''$).
4. BIS Standard: BIS strictly mandates First Angle Projection for all Indian educational and industrial engineering drawings.