# Braking Distance on Grade

Written by Jerry Ratzlaff on . Posted in Civil Engineering Braking distance on downgrade or upgrade, abbreviated as $$B_d$$, is when the highway is on a grade.  The steeper the downgrade the longer it takes to stop.  The steeper the upgrade the shorter it takes to stop.

## Braking Distance on downgrade or upgrade formulas

 $$\large{ B_d = \frac{ V^2 }{ 30 \; \left( \frac{ a }{ 32.2 } \;\pm\; G \right) } }$$ $$\large{ B_d = \frac{ V^2 }{ 30 \; \left[ \left(\frac{ a }{ 32.2 }\right) \;\pm\; \frac{ G }{ 100 } \right] } }$$

### Where:

 Units English Metric $$\large{ B_d }$$ = braking distance on grade $$\large{ft}$$ $$\large{m}$$ $$\large{ a }$$ = deceleration rate $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{sec}}$$ $$\large{ V }$$ = design speed $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{sec}}$$ $$\large{ G }$$ = grade percent divided by 100 $$\large{dimensionless}$$

## AASHTO Exhibit 3-2 Stopping Sight Distance on grade

 Design Speed Stopping Sight Distance Downgrade Upgrade 3% 6% 9% 3% 6% 9% 15 80 82 85 75 74 73 20 116 120 126 109 107 104 25 158 165 173 147 143 140 30 205 215 227 200 184 179 35 257 271 287 237 229 222 40 315 333 354 289 278 269 45 378 400 427 344 331 320 50 446 474 507 405 388 375 55 520 553 593 469 450 433 60 598 638 686 538 515 495 65 682 728 785 612 584 561 70 771 825 891 690 658 631 75 866 927 1003 772 736 704 80 965 1035 1121 859 817 782 