SME
Physical Geography
Landforms
Use this for “A to B crosses 5 contour intervals of 20 m and measures 5 cm on a 1:50,000 map. What are the gradient and slope angle?”
Diagram
Rise = n × CI = 5 × 20 m = 100 m.
Run
=
5
cm
×
50,000
100
=
2,500
m.
Gradient
=
100
×
rise
run
=
4%;
angle
=
tan⁻¹(
rise
run
)
=
2.29°.
This is an example. Type your own values to start a new problem.
CI
Contour interval
example · m
n
Intervals crossed
example
Δh
Rise
worked out (not typed) · m
dₘₐₚ
Map distance
example · cm
S
Scale denominator
example
d
Ground distance
worked out (not typed) · m
G
Gradient
worked out (not typed) · %
θ
Slope angle
worked out (not typed) · °
Formulas
Δh
=
n
×
CI
100 = 5 × 20
d
=
dₘₐₚ
×
S
100
2,500
=
5
×
50,000
100
G
=
100
×
Δh
d
4
=
100
×
100
2,500
θ
=
tan⁻¹(
Δh
d
)
2.2906
=
tan⁻¹(
100
2,500
)
Assumptions
•
The ground slopes evenly between the two points, so one gradient fits the whole line.
•
Contours close together mean steep ground; far apart, gentle ground.
•
The map distance is measured along the straight line from A to B; at 1:S, 1 cm on the map is S cm on the ground.
Step-by-step
WE KNOW
CI = 20 m, n = 5, dₘₐₚ = 5 cm, S = 50,000
FIND
rise (Δh), ground distance (d), gradient (G), slope angle (θ)
Step 1 · Find rise (Δh)
Use Δh = n × CI
Each interval crossed climbs one contour interval.
Δh = 5 × 20
Δh = 100 m
Step 2 · Find ground distance (d)
Use d = dₘₐₚ × S ÷ 100
Each
map
centimetre
stands
for
S
centimetres
of
ground;
÷
100
gives
metres.
d
=
5
×
50,000
100
d
=
250,000
100
d
=
2,500
m
Step 3 · Find gradient (G)
Use G = 100 × Δh ÷ d
Rise over run, as a percent.
G
=
100
×
100
2,500
G
=
10,000
2,500
G
=
4%
Step 4 · Find slope angle (θ)
Use θ = tan⁻¹(Δh ÷ d)
The slope angle is the angle whose tangent is rise over run.
θ
=
tan⁻¹(
100
2,500
)
100
2,500
=
0.04
θ
=
2.2906°
Check
Put the numbers back in. Both sides should match.
100 = 5 × 20 ✓
2,500
=
5
×
50,000
100
✓
4
=
100
×
100
2,500
✓
2.2906
=
tan⁻¹(
100
2,500
)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
Drainage density and bifurcation ratio
Use this for “A 75 km² basin has 180 km of streams: 40 of order 1, 9 of order 2 and 2 of order 3. Find its drainage density, bifurcation ratios and stream frequency.”
Landforms from their shape and process
Use this for “A valley has a flat floor and steep walls, with small valleys hanging high on its sides. What made it?”