This article examines the design limits of two attachment point segment skirt systems. By two point I mean that the skirt is only attached to a craft at an outer point and again at an inner point. There are no other intermediate attachments to the hull and the skirt on one side of the craft isn’t connected to the skirt on the other side.

In general , two point attachment skirts include bag skirts, straight segment skirts, extended segment skirts, loop segment and bag finger skirts. Jupe and C skirts are not included.

The analysis will look at straight segment skirts then apply those results to extended segment skirts. The result is applicable to all the skirt types mentioned and they will be the subject of future articles.

This article is not about the roll stiffness of a hovercraft. Roll stiffness is the ability of a craft to right itself when one side is deflected down. That response is a product of all the elements of the lift system – fan, ducting, compartmentalisation and skirt deflection.

This is an example of a straight segment. This form of segment is usually used as a finger on a bag and finger skirt and only had a brief usage in the late 60s as a whole skirt system.

An example of use

Terms

Outer face – that part of the skirt that is exposed to the atmosphere

Effective outer face – an area defined by a line from the outer attachment point to the ground contact point by the segment width

Assumptions

Pressure exerts a force perpendicular to a surface

Pressure on a surface results in a force perpendicular to the surface. Anywhere in space, pressure acts in all directions, but at a surface it appears as a force at right angles to the surface.

Another way of saying this is that pressure can’t make a surface slide sideways.

Distributed pressure force acts through a single point

The pressure on the outer face of the segment acts along the whole surface.

This net pressure force can be modeled as a single force acting through the centre of the area. i.e. through the middle of the outer face.

No compressive loads in the fabric

It’s fabric. It only resists tension. Compress it from the edges and it wrinkles and collapses.

External shape is not important

This is a free body analysis. The only important geometries are the lines from the inner attach, outer attach and the ground contact point. And to simplify even further, we’ll flatten the outer face.

Design principle

The external forces on the skirt are always balanced. No skirt fabric has compressive forces.

The analysis model

Based on the above assumptions, this is the profile for the flat straight segment as fitted to a hull.

Angle S is the profile angle of the outer face relative to ground at the ground contact point. As a starting point for this analysis, it is about 60Â°. For regular extended segments, this angle is around 45Â°. This straight segment would be a make-able segment but compared with the extended segment, the craft would have a much smaller hard structure clearance.

Forces on the segment

Force due to cushion pressure

There is an even pressure (cushion pressure) over the whole outer face. The net force is

\begin{aligned}
F_c&=P_c \times A &\\
\end{aligned}

where

F_c is the force on the outer face P_c is the cushion pressure A is the area of the outer face

\begin{aligned}
A&=l \times w &\\
\end{aligned}

where

l is the distance from the outer attachment point to the ground contact point w is the width of the segment

The force F_c acts in the middle of the line from the outer attachment point to the ground contact point.

Force at the inner attachment

The force at the inner attachment counters the pressure force and acts in a line from the inner attachment to the middle of the effective outer face.

In normal skirts the inner attachment force has a component that directly counters the cushion pressure force in size and direction and another component at right angles that tends to pull the skirt downwards. It is the second component that keeps the skirt under the craft and allows it to lift off.

Force at the outer attachment

The force at the outer attachment counters the downwards component of the inner attachment force. It’s a tension force.

This diagram shows each of the three external forces on a straight segment.

Force balance

The three external forces on the segment must be balanced. That means that a force in any one direction has to have forces in other directions to counter it. An unbalanced force means that the segment will move (relative to the hull). That’s something we don’t want to happen.

The three forces can be visualised as all acting through a point in the middle of the outer face. This point is a bit like the fulcrum of a balance.

The external forces on the segment at the mid point of the outer face, point M, look like this:

Any two of the three forces combine to exactly counter the third force. In engineering, we often use a force vector circuit to see that the forces are balanced.

Two of the forces have been shifted to create a circuit. The forces all balance. The skirt won’t move under changing cushion pressure.

Increasing the length of the segment

Next, we lengthen the outer face of the segment.

In practise, this would create geometries that can’t be made, so we’ll only examine the forces on the outer face like the previous two diagrams.

As we increase the length of the outer face, the size of the forces become larger but they remain in balance. The angle between the outer face and the direction of the force at the inner attachment point, angle A, becomes larger.

Eventually, when we extend the length enough, angle A becomes 90Â° and the force on the outer attachment point become zero. The only forces on the skirt are the equivalent force of the cushion pressure and the force at the inner attachment point.

If we extend the length of the outer face further, the force at the outer attachment has to become a pushing force to keep the forces in the segment in balance.

However, since the skirt is fabric and can’t withstand a compression force. It will just wrinkle and collapse.

This is a limit to the amount that the outer face can be lengthened.

Other skirt angles

Now to examine what happens when we change the angle of the outer face of the segment.

The same outcome occurs – the length of the outer face can be extended until the limit is reached and there is no force on the outer attachment on the outer attachment point.

Compared width previous example, the main difference is the lower hard structure clearance, the hover height. The forces are balance and at their limit but just at a reduced hover height.

If we repeat the analysis for many different angles, we find that each one has a different hard structure clearance.

Tracing the ground contact point G for different outer face angles results in a limit line.

The limit line

The limit line is a circular arc, centred on the inner attachment point, with a radius of the distance between the inner and outer attachment points. The line is the design limit for the ground contact point of a two point attached skirt.

This means that any segment that has a ground contact point outside the limit line is likely to collapse and won’t contain the air cushion. All straight segments will fall within the limit line.

The main implication of the line is that it sets a maximum theoretical hard structure clearance for a 2 point attachment system.

The maximum height is from the inner attachment point to the ground is the distance between the inner and outer attachment points.

Limits of extended segment geometry

In the previous analysis, we disregarded the physical practicality of making skirt shapes that verge on the limits of the geometry. Making a straight segment large enough to approach the limit line is almost impossible. The segment would perform poorly well before that limit. Straight segments also have the disadvantage that they reduce the cushion area and generally allow for less hard structure clearance compared with other skirt systems.

Straight skirts quickly evolved into extended segments, commonly used on many small hovercraft today.

Extended segments can be analysed in the same manner as straight segments.

If we make an imaginary cut in an extended segment from the outer attachment point to the ground contact, we create a straight segment and the extended part

The two elements can be separated for the purposes of the analysis. The element on the left is like a straight segment. If we imagine that there was a flat outer face across the cut, then we have the straight segment per the previous analysis.

If we add a flat face to the element on the right then we simply have a type of balloon – the pressure in the balloon is cushion pressure. The shape is distorted from a normal balloon shape by the other skirts around it and the tailoring of the outer shape. The pressure in the balloon is balanced by the tension forces in the skirt fabric and the imaginary flat face of the cut. In this model, the balloon doesn’t contribute to the forces at the attachment point.

Calling this type of skirt an extended segment is very appropriate – it simply extends the shape of the straight segment.

The limit of the ground contact point still applies. Extended segments allow the geometry of the skirt to approach the limit.

The limit line also explains why extended segments should be designed to be inboard of the outer attachment. If the ground contact point is designed to be outside the limit line there will be a point that the segment simply won’t retain the air cushion and the craft won’t lift off the ground.

Conclusions

However the limit line is applicable to extended segments (and all other 2 point attachment skirt systems).

Extended segment skirts have portions of their geometry outside the limit line.

The rules-of-thumb for the geometry of skirts have a sound basis in physics.

The interesting consideration is when the craft rolls or deflects sufficiently to move the ground contact outside the limit line.

The limit line is mathematical outcome of an analysis based on simplifying assumptions. Rather than being a precise line, it is more a region. As the geometry of the segment approaches the limit, the segment will bounce and deflect more. Skirts that are well past the line will simply not contain the air cushion and the craft will not lift off.

An example of an extreme segment

In the early 1970s, some oil storage tanks in England were moved by attaching a segmented skirt and floating the tank to it’s new location.

This is the only media I could find about the project, but I remember seeing a video of installing the segments. This project could only work because the distance between the upper and lower attachment points was large enough to allow the segment ground contact point to be lower than the underside of the tank.

The segment was fully contained within the limit line and would certainly be at a safe value at the ground contact point.

Non-dimensional skirt characteristics.

Two attachment point skirts can be characterised by a non-dimensional number:

l_{GC} is the distance from the inner attachment point to the effective ground contact point l_a is the distance between the inner and outer attachment points

The number represents the proximity of the ground contact point to the limit line and is commonly about 0.75 to 0.85 for well designed segment skirts.

## Introduction

This article examines the design limits of two attachment point segment skirt systems. By two point I mean that the skirt is only attached to a craft at an outer point and again at an inner point. There are no other intermediate attachments to the hull and the skirt on one side of the craft isn’t connected to the skirt on the other side.

In general , two point attachment skirts include bag skirts, straight segment skirts, extended segment skirts, loop segment and bag finger skirts. Jupe and C skirts are not included.

The analysis will look at straight segment skirts then apply those results to extended segment skirts. The result is applicable to all the skirt types mentioned and they will be the subject of future articles.

This article is not about the roll stiffness of a hovercraft. Roll stiffness is the ability of a craft to right itself when one side is deflected down. That response is a product of all the elements of the lift system – fan, ducting, compartmentalisation and skirt deflection.

This is an example of a straight segment. This form of segment is usually used as a finger on a bag and finger skirt and only had a brief usage in the late 60s as a whole skirt system.

An example of use

## Terms

Outer face– that part of the skirt that is exposed to the atmosphereEffective outer face– an area defined by a line from the outer attachment point to the ground contact point by the segment width## Assumptions

## Pressure exerts a force perpendicular to a surface

Pressure on a surface results in a force perpendicular to the surface. Anywhere in space, pressure acts in all directions, but at a surface it appears as a force at right angles to the surface.

Another way of saying this is that pressure can’t make a surface slide sideways.

## Distributed pressure force acts through a single point

The pressure on the outer face of the segment acts along the whole surface.

This net pressure force can be modeled as a single force acting through the centre of the area. i.e. through the middle of the outer face.

## No compressive loads in the fabric

It’s fabric. It only resists tension. Compress it from the edges and it wrinkles and collapses.

## External shape is not important

This is a free body analysis. The only important geometries are the lines from the inner attach, outer attach and the ground contact point. And to simplify even further, we’ll flatten the outer face.

## Design principle

The external forces on the skirt are always balanced. No skirt fabric has compressive forces.

## The analysis model

Based on the above assumptions, this is the profile for the flat straight segment as fitted to a hull.

Angle S is the profile angle of the outer face relative to ground at the ground contact point. As a starting point for this analysis, it is about 60Â°. For regular extended segments, this angle is around 45Â°. This straight segment would be a make-able segment but compared with the extended segment, the craft would have a much smaller hard structure clearance.

## Forces on the segment

## Force due to cushion pressure

There is an even pressure (cushion pressure) over the whole outer face. The net force is

where

F_c is the force on the outer face

P_c is the cushion pressure

A is the area of the outer face

where

l is the distance from the outer attachment point to the ground contact point

w is the width of the segment

The force F_c acts in the middle of the line from the outer attachment point to the ground contact point.

## Force at the inner attachment

The force at the inner attachment counters the pressure force and acts in a line from the inner attachment to the middle of the effective outer face.

In normal skirts the inner attachment force has a component that directly counters the cushion pressure force in size and direction and another component at right angles that tends to pull the skirt downwards. It is the second component that keeps the skirt under the craft and allows it to lift off.

## Force at the outer attachment

The force at the outer attachment counters the downwards component of the inner attachment force. It’s a tension force.

This diagram shows each of the three external forces on a straight segment.

## Force balance

The three external forces on the segment must be balanced. That means that a force in any one direction has to have forces in other directions to counter it. An unbalanced force means that the segment will move (relative to the hull). That’s something we don’t want to happen.

The three forces can be visualised as all acting through a point in the middle of the outer face. This point is a bit like the fulcrum of a balance.

The external forces on the segment at the mid point of the outer face, point M, look like this:

Any two of the three forces combine to exactly counter the third force. In engineering, we often use a force vector circuit to see that the forces are balanced.

Two of the forces have been shifted to create a circuit. The forces all balance. The skirt won’t move under changing cushion pressure.

## Increasing the length of the segment

Next, we lengthen the outer face of the segment.

In practise, this would create geometries that can’t be made, so we’ll only examine the forces on the outer face like the previous two diagrams.

As we increase the length of the outer face, the size of the forces become larger but they remain in balance. The angle between the outer face and the direction of the force at the inner attachment point, angle A, becomes larger.

Eventually, when we extend the length enough, angle A becomes 90Â° and the force on the outer attachment point become zero. The only forces on the skirt are the equivalent force of the cushion pressure and the force at the inner attachment point.

If we extend the length of the outer face further, the force at the outer attachment has to become a pushing force to keep the forces in the segment in balance.

However, since the skirt is fabric and can’t withstand a compression force. It will just wrinkle and collapse.

This is a limit to the amount that the outer face can be lengthened.

## Other skirt angles

Now to examine what happens when we change the angle of the outer face of the segment.

The same outcome occurs – the length of the outer face can be extended until the limit is reached and there is no force on the outer attachment on the outer attachment point.

Compared width previous example, the main difference is the lower hard structure clearance, the hover height. The forces are balance and at their limit but just at a reduced hover height.

If we repeat the analysis for many different angles, we find that each one has a different hard structure clearance.

Tracing the ground contact point G for different outer face angles results in a limit line.

## The limit line

The limit line is a circular arc, centred on the inner attachment point, with a radius of the distance between the inner and outer attachment points. The line is the design limit for the ground contact point of a two point attached skirt.

This means that any segment that has a ground contact point outside the limit line is likely to collapse and won’t contain the air cushion. All straight segments will fall within the limit line.

The main implication of the line is that it sets a maximum theoretical hard structure clearance for a 2 point attachment system.

The maximum height is from the inner attachment point to the ground is the distance between the inner and outer attachment points.

## Limits of extended segment geometry

In the previous analysis, we disregarded the physical practicality of making skirt shapes that verge on the limits of the geometry. Making a straight segment large enough to approach the limit line is almost impossible. The segment would perform poorly well before that limit. Straight segments also have the disadvantage that they reduce the cushion area and generally allow for less hard structure clearance compared with other skirt systems.

Straight skirts quickly evolved into extended segments, commonly used on many small hovercraft today.

Extended segments can be analysed in the same manner as straight segments.

If we make an imaginary cut in an extended segment from the outer attachment point to the ground contact, we create a straight segment and the extended part

The two elements can be separated for the purposes of the analysis. The element on the left is like a straight segment. If we imagine that there was a flat outer face across the cut, then we have the straight segment per the previous analysis.

If we add a flat face to the element on the right then we simply have a type of balloon – the pressure in the balloon is cushion pressure. The shape is distorted from a normal balloon shape by the other skirts around it and the tailoring of the outer shape. The pressure in the balloon is balanced by the tension forces in the skirt fabric and the imaginary flat face of the cut. In this model, the balloon doesn’t contribute to the forces at the attachment point.

Calling this type of skirt an

extendedsegment is very appropriate – it simply extends the shape of the straight segment.The limit of the ground contact point still applies. Extended segments allow the geometry of the skirt to approach the limit.

The limit line also explains why extended segments should be designed to be inboard of the outer attachment. If the ground contact point is designed to be outside the limit line there will be a point that the segment simply won’t retain the air cushion and the craft won’t lift off the ground.

## Conclusions

However the limit line is applicable to extended segments (and all other 2 point attachment skirt systems).

Extended segment skirts have portions of their geometry outside the limit line.

The rules-of-thumb for the geometry of skirts have a sound basis in physics.

The interesting consideration is when the craft rolls or deflects sufficiently to move the ground contact outside the limit line.

The limit line is mathematical outcome of an analysis based on simplifying assumptions. Rather than being a precise line, it is more a region. As the geometry of the segment approaches the limit, the segment will bounce and deflect more. Skirts that are well past the line will simply not contain the air cushion and the craft will not lift off.

## An example of an extreme segment

In the early 1970s, some oil storage tanks in England were moved by attaching a segmented skirt and floating the tank to it’s new location.

This is the only media I could find about the project, but I remember seeing a video of installing the segments. This project could only work because the distance between the upper and lower attachment points was large enough to allow the segment ground contact point to be lower than the underside of the tank.

The segment was fully contained within the limit line and would certainly be at a safe value at the ground contact point.

## Non-dimensional skirt characteristics.

Two attachment point skirts can be characterised by a non-dimensional number:

where

l_{GC} is the distance from the inner attachment point to the effective ground contact point

l_a is the distance between the inner and outer attachment points

The number represents the proximity of the ground contact point to the limit line and is commonly about 0.75 to 0.85 for well designed segment skirts.

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