If you have been asked to stakeout or calculate the horizontal offset to a design batter in the field, but do not have any of the survey road alignment applications (like Leica’s roadrunner) on your survey controller that would automate the calculation for you, I will explain below how you can calculate this yourself in the field.
The Formula
The formula to calculate the offset horizontal distance from the design batter face is: (Tan (90 – Ɵ)) * RL Cut +/– O/S = x
The known variables for the above formula are:
- Design grade in degrees of the batter (Ɵ).
- Elevation above the design batter toe (RL Cut).
- Distance offset from the batter toe (O/S). You will have to observe which side of the batter toe you are on, inside of the batter or outside of the batter, which will determine if you + or – the offset distance from the batter toe from the calculation.
The formula calculates the “opposite side” of the triangle which is made up of the batter face (hypotenuse) and RL difference to the batter toe point (adjacent side). See the below image for a visual explanation of the previous sentence. You then minus or plus your offset distance to the design toe of the batter depending on what side you are on.
Continue reading for a further explanation about this calculation and some diagrams which, if you are anything like me, will help visualize and understand the calculation.
The two diagrams below will explain the above formula.
Inside the Batter Toe Line
If you are inside of the batter toe line, the formula to calculate the offset to the batter face is: (Tan (90 – Ɵ)) * RL Cut – OS = x
An example calculation of this would be:
| Variable | Value |
|---|---|
| Ɵ | 65° |
| RL Cut | 15m |
| O/S | 2.5m |
- (Tan (90 – Ɵ)) * RL Cut – O/S = x
- (Tan (90 – 65°)) * 15m – 2.5 = 4.495 offset from the surveyed position to the batter face.
Outside the Batter Toe Line
If you are outside of the batter toe line, the formula to calculate the offset to the batter face is: (Tan (90 – Ɵ)) * RL Cut + O/S = x
An example calculation of this would be:
| Variable | Value |
|---|---|
| Ɵ | 65° |
| RL Cut | 15m |
| O/S | 2.5m |
- (Tan (90 – Ɵ)) * RL Cut + O/S = x
- (Tan (90 – 65°)) * 15m + 2.5 = 9.495 offset from the surveyed position to the batter face.
