# Tension in a catenary curve - Cable Camera

• Justtoots
In summary: Here they are:"When calculating (T), am I correct in assuming that is the cable tension and would thus be the equivalent tension at each of the anchors? "Yes, (T) is the cable tension.
Justtoots
Hi, my problem is this; I am designing a cable camera system to film downhill pursuits. I need to calculate how much tension is required to hang a cable over a 100m span with no more that 0.5m sag in the middle, when is it fixed at two point, both at the same hight. From the research I have done I have found out that a catenary curve will calculate the sag in a chain when subject to gravity. I am having trouble working through the equations associated with this and would appreciate some help working though it with me.

Many thanks in advance,

Alex T

What kind of chain? What is it's mass per unit length? Is a camera going to be hung from this chain? What is the mass of the camera and its attachments? Does the sag criterion apply with or without the camera being suspended from the chain?

"What kind of chain? What is it's mass per unit length? "

This is the specification of the cable;

DIN 3055 2mm
Steel C7 ( Mn + Si) , hot-dip galvanized with 1770 N / mm nominal strength
SPECIFICATIONS:

Cable diameter 2.0 mm
Construction 6x7 + FC
Tensile strength of 1770 [N/mm2 ] [ Mpa ]
Weight / meter 0.0146 kg
Breaking load 260 kg

"Is a camera going to be hung from this chain? "

Yes, the idea is that I will build a carriage which will be remote controlled with a drive motor to run the length of the cable.

"What is the mass of the camera and its attachments? "

The total weight of the carriage plus camera is, 1.26Kg

"Does the sag criterion apply with or without the camera being suspended from the chain? "

The sag needs to be calculated with the camera applied to the cable. My aim is to know what tension need to be applied to the cable so that when then camera travels up and down the cable, it does not sag to much that it hits the ground.

SteamKing said:
Adding a weight to the cable changes the problem somewhat. It becomes similar to analyzing what happens to a cable tramway:

http://www.tramway.net/Advanced Equations.pdf
Hi SteamKing,

I hope justtoots was able to work out his calculation.

I found myself using the cable tramway equations for a simple suspension bridge I want to build in my backyard. I had to convert my Aussie metric to Imperial to use the stress curve tables on page 156 & 157. Are you aware of an online calculator that I could use in place of the tables? Also, when calculating (T), am I correct in assuming that is the cable tension and would thus be the equivalent tension at each of the anchors? I was also wondering if (T) was measured in pounds force?

Guy L'Estrange said:
Hi SteamKing,

I hope justtoots was able to work out his calculation.

I found myself using the cable tramway equations for a simple suspension bridge I want to build in my backyard. I had to convert my Aussie metric to Imperial to use the stress curve tables on page 156 & 157. Are you aware of an online calculator that I could use in place of the tables?

No, I'm not familiar with any such online calculators.

Also, when calculating (T), am I correct in assuming that is the cable tension and would thus be the equivalent tension at each of the anchors? I was also wondering if (T) was measured in pounds force?

I would not advise using these equations to design a suspension bridge. These equations are intended for use in analyzing tramways, i.e., vehicles suspended from a cable, and are not necessarily applicable to designing suspension bridges.

IIRC, justtoots was trying to suspend a camera from a long cable and limit the sag in the span due to the weight of the camera. If he miscalculated, he was out the price of a new camera.

In your case, you want to build a suspension bridge to be used by people, so if you miscalculate, someone could get hurt.

In this circumstance, I urge you to seek the advice of a qualified engineer who can inspect your site and discuss with you what sort of bridge you plan to build. There may be local building codes which also must be satisfied, and the engineer you select should be familiar with these codes. The engineer can design the structure you need and help in the selection of the proper materials and methods of construction.

Good Luck!

billy_joule
Thanks SteamKing. I will get an engineer to look over my calcs before construction. I'm just one of those people who likes to know how things work the way they do. I found a resource on the tramway.net site that has equations for the type of suspension bridge I want to build.

## 1. What is a catenary curve?

A catenary curve is a mathematical curve that describes the shape of a hanging cable or chain under its own weight, suspended between two fixed points. It is similar in shape to a parabola, but is a more accurate representation of the curve formed by a hanging chain or cable.

## 2. How does tension affect a catenary curve?

Tension is a key factor in determining the shape of a catenary curve. As tension increases, the curve becomes more shallow and flattened, while a decrease in tension results in a steeper curve. This is because tension acts to pull the curve taut, creating a more straight-line shape.

## 3. What role does gravity play in a catenary curve?

Gravity is the main force that contributes to the formation of a catenary curve. The weight of the cable or chain itself, combined with the force of gravity, creates a downward pull that causes the curve to sag. The resulting shape of the curve is a balance between the pulling force of tension and the downward force of gravity.

## 4. How is tension measured in a catenary curve?

Tension is typically measured as a force in newtons (N) or pounds (lbs). In the context of a catenary curve, tension can be measured at any point along the curve by suspending a weight or load from the cable and measuring the force required to keep the cable in place.

## 5. How is a catenary curve used in cable camera systems?

Catenary curves are commonly used in cable camera systems to support and guide the camera cable. The curve allows the cable to span a distance between two fixed points without the need for additional support structures, creating a smooth and stable path for the camera to travel along. Tension is carefully monitored and adjusted to ensure the cable remains taut and the curve maintains its shape.

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