SME
Transportation Engineering · Problem type
Minimum radius of a horizontal curve
Use this for “A curve on a 100 km/h highway is banked at e = 0.08 with side friction f = 0.12. What is the smallest radius it may have?”
Diagram
Rₘᵢₙ
=
V
2
127(e + f)
Rₘᵢₙ
=
100
2
127 × (0.08 + 0.12)
Rₘᵢₙ = 394 m
The bank e and the tyres’ side friction f hold the car on the curve.
The arc is drawn to scale over 50° to show the radius.
This is an example. Type your own values to start a new problem.
Rₘᵢₙ (m)
=
(
V (km/h)
)
2
÷
(127
×
(
e
+
f
))
Formulas
Rₘᵢₙ
=
V
2
127 × (
e
+
f
)
393.7008
=
100
2
127 × (0.08 + 0.12)
Assumptions
•
The car rounds the curve at the design speed; the bank e and side friction f are decimals.
•
e plus f together supply the push toward the curve’s centre (point-mass model).
•
V in km/h gives R in metres: 127 is 3.6² × 9.81.
Step-by-step
WE KNOW
V = 100 km/h, e = 0.08, f = 0.12
FIND
minimum radius (Rₘᵢₙ)
Step 1 · Find minimum radius (Rₘᵢₙ)
Use Rₘᵢₙ = V² ÷ (127 × (e + f))
A
tighter
curve
needs
more
push
toward
the
centre;
the
bank
and
the
tyres
can
give
only
e
+
f
of
it.
Rₘᵢₙ
=
100
2
127 × (0.08 + 0.12)
Rₘᵢₙ
=
100
2
127 × 0.2
Rₘᵢₙ
=
100
2
25.4
Rₘᵢₙ
=
10,000
25.4
Rₘᵢₙ = 393.7008 m
Check
Put the numbers back in. Both sides should match.
393.7008
=
100
2
127 × (0.08 + 0.12)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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