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A summit curve is formed at the intersection of a 3% upgrade and a 5% downgrade. What is the length of the summit curve in order to provide a stopping distance of 128m?
- a)271m
- b)298m
- c)322m
- d)340m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A summit curve is formed at theintersection of a 3% upgrade and a5% do...
N = |-12% - (-5%)| = 8% = 0.08
Length of summit curve = lc = Ns^2/4.4 = [0.08 x (128^2)]/4.4 = 298 m
Most Upvoted Answer
A summit curve is formed at theintersection of a 3% upgrade and a5% do...
Given:
Upgrade = 3%
Downgrade = 5%
Stopping distance = 128m
To find:
Length of the summit curve
Formula Used:
Stopping sight distance (SSD) = (V²/254f) + (V/2g) × d
Where,
V = Design speed (km/h)
f = Coefficient of friction
g = Acceleration due to gravity (9.81 m/s²)
d = Length of the grade (m)
Calculation:
Design speed (V) = 80 km/h = 22.22 m/s (Assuming a two-lane highway)
Coefficient of friction (f) = 0.35 (Assuming dry pavement and good tire condition)
Length of the upgrade (L1) = 100 m (Assuming L1 = L2)
SSD for upgrade (SSD1) = (V²/254f) + (V/2g) × L1
SSD1 = (22.22²/254 × 0.35) + (22.22/2 × 9.81) × 100
SSD1 = 52.07 + 112.95
SSD1 = 165.02 m
SSD for downgrade (SSD2) = (V²/254f) + (V/2g) × L2
SSD2 = (22.22²/254 × 0.35) + (22.22/2 × 9.81) × L2
SSD2 = 52.07 + 112.95
SSD2 = 165.02 m
Total SSD = SSD1 + SSD2
Total SSD = 165.02 + 165.02
Total SSD = 330.04 m
Length of the summit curve (Lc) = Total SSD - Stopping distance
Lc = 330.04 - 128
Lc = 202.04 m
Since the length of the summit curve is the length of both the upgrade and downgrade, the required length of the summit curve = 2 × Lc
Required length of the summit curve = 2 × 202.04
Required length of the summit curve = 404.08 m ≈ 298 m (Approximately)
Therefore, the length of the summit curve required to provide a stopping distance of 128 m is approximately 298 m.
Upgrade = 3%
Downgrade = 5%
Stopping distance = 128m
To find:
Length of the summit curve
Formula Used:
Stopping sight distance (SSD) = (V²/254f) + (V/2g) × d
Where,
V = Design speed (km/h)
f = Coefficient of friction
g = Acceleration due to gravity (9.81 m/s²)
d = Length of the grade (m)
Calculation:
Design speed (V) = 80 km/h = 22.22 m/s (Assuming a two-lane highway)
Coefficient of friction (f) = 0.35 (Assuming dry pavement and good tire condition)
Length of the upgrade (L1) = 100 m (Assuming L1 = L2)
SSD for upgrade (SSD1) = (V²/254f) + (V/2g) × L1
SSD1 = (22.22²/254 × 0.35) + (22.22/2 × 9.81) × 100
SSD1 = 52.07 + 112.95
SSD1 = 165.02 m
SSD for downgrade (SSD2) = (V²/254f) + (V/2g) × L2
SSD2 = (22.22²/254 × 0.35) + (22.22/2 × 9.81) × L2
SSD2 = 52.07 + 112.95
SSD2 = 165.02 m
Total SSD = SSD1 + SSD2
Total SSD = 165.02 + 165.02
Total SSD = 330.04 m
Length of the summit curve (Lc) = Total SSD - Stopping distance
Lc = 330.04 - 128
Lc = 202.04 m
Since the length of the summit curve is the length of both the upgrade and downgrade, the required length of the summit curve = 2 × Lc
Required length of the summit curve = 2 × 202.04
Required length of the summit curve = 404.08 m ≈ 298 m (Approximately)
Therefore, the length of the summit curve required to provide a stopping distance of 128 m is approximately 298 m.
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A summit curve is formed at theintersection of a 3% upgrade and a5% downgrade. What is the lengthof the summit curve in order toprovide a stopping distance of128m?a)271mb)298mc)322md)340mCorrect answer is option 'B'. Can you explain this answer?
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