# Level vs inclined spans

What difference does uneven attachment heights in a span make to tension?

We can approach this issue by comparing tensions in two spans identical except for the vertical height difference. Equations are from AS/NZS7000:2016

For this worked example the spans have these common properties:

• Krypton conductor, weight 0.433 kg/m
• Conductor breaking load 37.4 kN
• 60m span
• strung at 10% CBL at 15°C, standard temperature 15°C

Stringing tension at 10% CBL is 3.74 kN = 3740 N

W (mass/meter) = 0.433 × 9.81 = 4.248 N/m

Catenary constant $$C=\frac{H}{W}\tag{R8}$$

C = 880.47 m

Conductor catenary length $$S=\sqrt{\left ( 2C sinh\frac{L}{2C} \right )^{2}+h^{2}}\tag{R21}$$
S = 60.012 m ie only 12mm longer than the span length. Of course the conductor does not hang exactly in keeping with the theoretical prediction due to a number of factors.

Sag $$D \approx \frac{IC}{L}\left ( cosh\frac{L}{2C}-1 \right )\tag{R37}$$

D = 0.5111 m

Back calculating tension $$H=\frac{WL^{2}}{8D}\tag{R12}$$

H = 3739.6 N

Performing the same calculations with the addition of the vertical height difference in the span attachment points of 1.5m gives:

C = 880.47 m
S = 60.030 m
D = 0.5113 m
H = 3738.5 N

You will see that all calculated values are essentially the same within any practical limits for a power line.

To answer the initial query, assuming a level span or having (slightly) uneven attachment heights does not affect tensions.

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