Steve Temple Storm Report
Back to Impington Windmill, SPAB
Storm Report
Introduction
“Watter is the great enemy of Windmills” – Chris Wilson. Well, there’s a lot of truth in this much loved saying, but at best it only accounts in part for two of the recent events. Storm Ciara dealt blows to at least four mills, stripping sails off Ibstone and Bocking mills, braking the brakewheel at Soham Downfield and decapitating Burgh le Marsh. Of these, Chris’s adage may well have applied to Ibstone and Bocking where it was known that the sails in question were decaying presumably from ingress of water, but the cases of Burgh le Marsh and Downfield were entirely caused by the wind itself. Or were they?
When an aircraft crashes, there is a serious and complex investigation into the causes with the single purpose of trying to prevent a recurrence. Often the findings of these investigations attribute multiple causes, many of which would have been insufficient in themselves. It is part of the philosophy of these investigations that they are not trying to apportion blame – though, of course, that is what the lawyers want them to do. Even in the many cases where pilot error is the primary cause, the investigations look behind these errors at, for example, training programmes and unclear flight procedure manuals.
It seems to me that we need this sort of approach when it comes to windmill accidents. The consequences are hardly in the same league, but to the owners and lovers of the mills they are tragedies and we should learn from them. They cost money – often unnecessarily and to the detriment of the many mills seeking funding for more mundane but very necessary work.
Background
I’m often driven by intellectual curiosity to see if I can explain difficult phenomena. Some years ago, I wanted to find out how much power my mill at Impington could have produced in its heyday. I built a model of the wind forces in Excel and eventually plotted a power diagram which related the power to the wind speed and the angle of the shutters. Last year, Jim Bailey of Heckington Mill described their tail winding event, and I immediately thought that it might be possible to model this in my spreadsheet – but I didn’t take any action then. Also, I was reminded that my mill had once turned suddenly through 90° when I was out. It had a locked fan tail at the time, and no sails, so I can only presume that it must have been moved by wind side forces on the fan itself.
On the Sunday of Ciara, Andrew Kite at Soham Downfield rang me to say that his brakewheel had been broken by the wind despite having been spragged to stop it turning. In fact, the sprag (an RSJ) had been bent! Later that day, I heard about Burgh le Marsh with the initial reports that it had been turned downwind and then the cap blown off.
So, I turned to my wind forces spreadsheet and have been working on it to try to explain what happened.
Anecdotal evidence
Jim, who was present in Heckington at the time of their tail winding, said that it sounded like a machine gun going off. He also said the fan tail was down for repairs, so that the mill was not winding automatically. This was also the case at Burgh le Marsh – the first press photos showed the fan on the ground beside the mill (having clearly not fallen from a great height). Later, at the Mills Section committee I learnt that the fan had been down for repairs during the winter.
It may seem obvious that a mill without its fan is liable to tail winding, but in both the cases at Heckington and Burgh le Marsh, and in mine at Impington, the cap was restrained from winding by engagement with the fan gear train, and this was locked to prevent turning. This implies that the gears must have “jumped” (been forced out of engagement) and then bumped along the rack as the wind pushed the sails round. This would explain the sound that Jim described. But would the wind have been strong enough to do this?
At Soham, discussing it with Andrew, I realised that he had only spragged the Brakewheel in one direction, against the natural rotation of the sails. I felt then that the torque produced with shutters open and the mill winding properly could not be sufficient to do so much damage, particularly bending a substantial and fairly short RSJ. I guessed that what had happened was that the sails had first turned a little backwards, away from the restraint of the RSJ and then accelerated forwards, gaining sufficient momentum to smash the wood work against the RSJ and bend it as well. An hour later, I watched my mill during the early stages of Ciara, and could see that it was trying to turn in both directions as gusts hit it. The brake was on, but no other constraint – and the brake is not good at stopping the sails going the wrong way. I often observe that, in high winds, the sails will creep round gradually in the wrong direction. Following that observation, Andrew used ratchet straps to lock the brakewheel in place against rotations in both directions, and no further damage followed even at the height of Ciara over the remainder of the day.
I decided that I had to try to assess the scale of forces produced by the wind, particularly in gusty conditions
Some Aerodynamics
Lift and Drag
The forces on a wing are analysed by calculating Lift (always perpendicular to the airflow) and Drag (along the airflow). A flat surface facing the airflow brings it to a full stop and exerts a pressure proportional to the density of the air and the velocity2. The aerodynamics of a an aerofoil can be described using a Lift Coefficient (cl) and a Drag Coefficient (cd) which give the proportion of this full stop pressure plotted against the angle of the flat surface to the airflow – the Angle of Attack (AoA). Usually this relationship is plotted for a limited range of AoA – up to the point where the wing “stalls” with a consequential reduction in lift and sharp increase in drag. I found a paper published by Sandia National Labs that plots the behaviour of a flat wing through a full range of AoA from 0 to 180°. Here it is.
This is what we need in order to describe the full wind forces on a mill when the wind comes from unexpected directions. Notice that the cl increases rapidly until the AoA reaches 15° when it drops suddenly. This is the point at which aeroplanes tend to give up and fall out of the sky. But windmills have to put up with every possibility!. When the AoA is 90°, the plate is at right angles to the flow, and there is only drag, no lift. This is the case for a tail winded mill with the shutters fully closed, and it is the condition when the cap gets torn off. There after, as the angle increases, the lift works in the opposite direction – this can also happen to a windmill when the gusts overcome the shutters.
Using this data, the lift and drag forces on each shutter and other surfaces on the sails can be calculated once we know the AoA.
Gusts
If the wind were steady and the mill pointing into the wind, then there would be no side forces to cause the cap to turn down wind. What might initiate such a turning force would be a relative angle between the wind and the fore-aft axis of the mill. Obviously, this can arise if the mill is not winding properly, but it can also occur with a properly winding mill if the wind direction changes substantially and quickly.
It is also not obvious as to what the nature of “gusts” is. In an airflow, any obstacle is likely to give rise to vortices: you can see this effect in the flow of a river – Leonardo da Vinci observed and drew this. Here is a picture of the flow behind an island in the Indian Ocean, showing a sequence of alternating vortices shedding from the island and extending as high as cloud level. Each vortex is many kilometers in diameter.
Such vortices have a rotational speed that just about matches the average speed, and, standing at a point downstream, you would see a combination of the rotational speed and the average speed looking like this:
The speed varies from zero (a lull) to twice the average, and the direction varies ±90° either side of the average. The orange line shows the envelope of the wind at any moment as the vortices roll by, and the green line shows a typical resultant wind at the mill. Some weather forecasts give expected gust levels as a maximum speed, usually around 2x the average speed, but don’t quote the variation in direction. Gusts occur at all scales, from a few cm across (arising from trees and chimneys) to 10s of km (from hills and large terrain features and also from thermal activity).
In the results from the SPAB anemometer at Impington for storms Ciara and Dennis the average and maximum speeds vary in the range quoted above:
The wind directions vary less than predicted by the vortex model, but the anemometer only samples every 10 min, so that it doesn’t capture short duration gusts. Moreover, it only records the average, whereas it captures the maximum wind speed (the pink line) as well as the average (blue). Note that the maximum is usually 2x the average, as predicted by the rolling vortices theory. The highest speed in both storms just reached 25 m/sec (with an average speed of 12.5 m/s), and this is the value I have used for analysis. I have assumed that the gust model of wind direction applies, too.
At a mill, even if it is winding properly, there will always be a difference between the wind direction and the pointing direction of the mill because the winding process takes time and requires there to be a difference in order to turn the fan. My mill takes about 40 sec to align itself to a change in direction and during this time the wind direction will be at a large angle to the mill pointing direction. This then gives rise to off-axis lift and drag forces that produce a torque that will try to turn the cap. On the Lincolnshire mills, which all use a dead curb (no wheels or rollers) the angle of the wind must be greater to initiate a large enough winding torque to overcome the friction.
Some Mechanics
Modeling the forces on the sails of a mill is not easy: the geometry is complex, involving various different directions and distances in all three axes, and the wind flow varies in speed and direction in the horizontal plane. As the wind changes, the angle at which it meets the various surfaces changes, and we need to know what this angle is to give us the AoA and hence the lift and drag forces on each element using the flat plate aerofoil graph above). The drag direction is always aligned to the wind, but the lift is perpendicular to both the wind and the intersection of the wind plane and the surface.
Mathematically, the language which describes all this is called Vector Algebra: a vector has both direction and size and is defined by giving its “components” along the x, y and z axes. Once everything is defined by vectors, which can describe geometry, velocity, force or moments, the algebra can derive relative directions between two vectors and the size of the resultant combination. All this can be handled in a spreadsheet, ending up with the calculated total force and total moment due to sum of the lift and drag on all the components. In particular, we want to calculate the vertical lift force (tending to tilt / remove the cap), the horizontal force on the curb (affecting the meshing of gears and also stressing the tower) and the torque about the vertical axis (tending to rotate the cap). To look at the Downfield problem, we also need to calculate the torque around the windshaft.
Such results would then provide us with inputs to further calculations such as the bending moment on the sails (causing them to snap), and the forces on the gear teeth of the winding mechanism to see if the gears might jump.
Winding Arrangements
There are major differences between the final winding drives on the different mills.
On mine, the gear ring on the tower is horizontal, with the final drive pinion having a horizontal axis and the teeth meshing along a horizontal line. This means that the weight of the cap keeps the teeth in mesh, and it also means that errors in the circularity of the curb and the cap affect the length of tooth in mesh at different points around the circumference, with at least 1” variation. However, the depth of the tooth engagement is pretty well constant even if the curb is not completely flat. There is no vertical constraint on the cap, so that, if the lift force exceeds the weight of the cap, then it will blow off.
The Lincolnshire mills’ winding system uses a vertical gear ring mounted on the inside of the tower. This means that any errors in circularity will affect the depth of meshing, and also that the principle force keeping the gears in mesh is due to the wind force fore-aft. There is a vertical restraint on the cap formed by a flange on the gear ring engaging with truck wheels which centre the cap and help to prevent it blowing off, so that the lift force necessary to remove the cap must exceed the weight by some amount in order to cause the cap to tip off.
In all cases, the horizontal forces due to the wind are resisted by the top of the tower, and are concentrated at points where the truck wheels come into contact. This puts potentially very high loads at these points, and they are the places where damage will start. The worst such place will be in the direction of the sum of the side force and the fore-aft force, and this point will move continuously during gusts – no point on the tower is safe!
Forces on Gears
Gear teeth are designed to make contact with each other at a “pressure angle” – usually 20°. However, two effects can increase this angle quite dramatically. First, because the tooth faces are curved, for gears which are partially out of mesh, this angle increases as the very tips of the gears come into contact. Second, the last gear in the winding train is often very small. Below is a picture of Sibsey mill, which only has 10 teeth on this last gear. Inevitably, the tips are pointing at 18° plus the pressure angle. Looking at this picture, I would estimate that the angle is of the order of 45°. This contact angle means that, if the gears are subject to an external force trying to overcome them in the turning direction, then there is also a force trying to separate them, and at 45° this disengaging force is equal to the applied force. In the case of a vertical curb on the inside of the mill, as at Heckington and Burgh le Marsh, this disengaging force acts to push apart the final gear shaft and the curb itself. In the case of a vertical curb on the outside of the tower as at the Great Mill at Haddenham, the disengaging force on the gears is added to the wind force, and in the case of horizontal teeth as at Impington, the disengaging force is opposed by the weight of the cap. At Heckington et al, the worst point of application of this force is at the junction of adjacent segments of the curb (rather like the gaps in the rail of an unwelded railway) Such a point can be seen in the picture below just to the right of the spur gear. At Haddenham, many of the segments are mobile (in the dentist’s sense) and cannot resist this force to any great extent. Such is the size of the force that on several of the segments, the casting has cracked at the central bolt hole, leaving the two ends almost floating free. None of this bodes well for prevention of an unexpected tail winding event.
Once the total force applied to the mill is known, these different configurations each lead to a separate calculation for estimating whether the gears will jump and allow accidental winding of the cap.
Onset of Winding
To initiate winding of the mill that is approximately aligned to the wind direction, the gusts must produce enough torque to, overcome the engagement of the winding gear with the curb and cause the teeth to jump. Once an initial movement has taken place, the now offset angle to the wind has to be added to the gust deviation – so that a similar gust will further turn the cap, and the catastrophe progresses. Thus, the all important question is whether the gustiness is able to start the process going, and that is what I aim to calculate.
Some Geometry
The following sketch shows the geometry which I have used to calculate the forces. The shutters have been represented by two “sails” of the total area of the shutters, placed halfway along the bays on each side of the windshaft. The sail plane is perpendicular to the stock – implying that the shutters are constrained at an angle of 90° by the striking gear. This will be true even if the striking lever is not locked, because, for off-centre winds, the rotations of the shutters on each of the pair trying to follow the wind are in the same direction and therefore opposed by the fork irons which normally operate the shutters in opposite directions. In extremes, one of the fork irons may buckle, allowing the shutters to close. This happens on both Impington and Burwell for quite modest tail winds.
I have ignored the forces on the stocks and sail frames because these provide a total area that is only a small fraction of the shutter area. I have also ignored the weather of the sail because I am assuming that the shutters are perpendicular to the stocks, so that the twist does not affect the angle at which the wind intersects them. So, all shutters on one sail are at the same AoA to the wind for any condition of the combined wind direction and the sail angle to the horizontal.
Opposing pairs of sails like this can only produce forces centred on the poll end of the windshaft, but offset from the fore-aft centerline by the angle of the wind. In the case of Burgh le Marsh, which has 5 sails, asymmetric forces are produced, but the asymmetry will be quite small, so I have simplified the layout to symmetrical pairs.
At Impington I have 4 sails, so both pairs need to be calculated separately. When the sails are set at 0 and 90°, the horizontal sail will produce a side force (in the y direction) but no vertical force, and the upright sail will produce both a side force and a lifting force. With the sails at 45°, both pairs act equally to produce both a side force and a lift force on the cap. We only need to calculate for angles between 0 and 45° - all other cases are then represented.
Heckington has 8 sails, 4 pairs, so only needs to be calculated for 0 to 22.5°
I have modeled Impington and Heckington, for simplicity, and using Impington data for aspects such as the weight of the cap, which I don’t have for Heckington. Burgh le Marsh would be similar to Impington, but with the extra sail both smoothing out the fluctuations arising from different positions of the sails and with the additional out-of-balance force.
Calculation Results
Heckington and Burgh le Marsh Tail Winding
Using data for Heckington, here is a graph showing the winding torque applied to the sails for a range of gust angles and sail angles. This shows, amongst, other things, how complex the situation is – with substantial variation in the forces, sometimes in unexpected ways. However, it allows us to pick the worst cases and calculate the likelihood of any of the events described in the opening paragraphs.
The 8 sails give a fairly uniform set of moments as the sail angle varies from 0 – 22.5° when the next sail round is in the 0 position. There is little variation along this axis as a result of the large number of sails. The maximum winding torque occurs along the gust angle of 30°, (corresponding to a net wind direction of 15°), and is around 3.5 Tonne metres in magnitude – that’s a pretty big winding force.
Notice that the winding torque reduces as the gust angle increases from about 30° where it peaks. This is the effect known as “quartering” the mill to minimise the forces. I think this is deceptive, because the gust velocity is reducing as the gust angle increases (see graph of gust vectors). However, if the mill were set at 90° to the wind, then the side forces, and hence turning moment would be due to the wind working at the maximum speed of 2x its average – so the forces would be around 4x greater than sown here.
The force applied tangentially to the winding gears and curb at the worst point is 1.07 T after allowing for the friction forces on the curb. The radial separation force is the same, as described above.
Whilst this is a substantial force, it is at least possible that it would not force the gears apart and allow accidental winding. However, it seems to me to be marginal – I am quite confident that the damaged curb at Haddenham would give way under such a force.
Noting that Impington has horizontally orientated gear teeth, the weight of the cap holding the final gear and curb together is considerably greater than the vertical separation force on the gears. Consequently, accidental tail winding of this type would be extremely unlikely to happen.
Value of the fantail
Of course, the fantail would normally wind the mill to re-align it during a gust, but, as stated above, this effect does not happen instantly, so we should assume that the accidental winding tendency would happen even with a working fantail in place. The balancing moment from the fantail obviously depends how far the fan is from the rear of the curb. In the case of Impington, there is a considerable overhang, so that the fantail can apply an opposing winding torque in the manner of a weather cock even when it’s not turning itself: and this just about balances the torque due to the sails, so that even its passive presence would obviate the risk of tail winding. Please note that not all mills are as fortunate as mine in this respect.
8 sails versus 4 sails
This is the same graph as above using data for Impington with its parsimonious 4 sails.
It looks quite similar, with almost the same worst case of 3.7 Tm winding torque, but with more variation as the sail angle changes. It is noticeable both that the winding torque is reduced for the sail pairs at 0° and 90° - the St George’s Cross position - where it is “only” 2 Tm and, also, that the worst case is when the sails are at 25° and 115°, both with gust angles of 45°. So, for 4 sailed mills, it’s safest to park them in the St George’s cross position – but still not very safe!
Decapitating forces
At no point does the lift force on the sails exceed the total weight of the cap and sails on either Heckington or Impington. I always assumed that this would be the mechanism by which caps got torn off, but this is not shown by this analysis. This statement is true even if the mill is tail winded and the shutters forced closed.
However, for a tail winded mill the horizontal (sliding) forces peak at around 5 T, and even allowing for the friction between the cap and the curb, this leaves more than 4 T applied as a point load to the most loaded truck wheel. I think it very unlikely that a brick tower would survive this. Wooden structures are much more resilient, and could well survive. At Impington, the truck wheels press against a continuous band of metal, so that the load is distributed locally and minimizes the stress on joints in the wood work. Where the truck wheels engage directly with the curb as at Heckingtonand Burgh le Marsh, at some point during a gust the forces will be applied to a weak point as described for Sibsey mill, and it would be unlikely that a bolt drilled down into the brick or even the brickwork itself would survive.
The cap will not tip off, but it will slide off the tower.
Stock Breaking
Looking at Ibstone’s and Bocking’s problems, the calculation gives us the individual forces on the sails and hence the moments trying to break the stocks at the canister. This bending moment amounts to about 3.8 Tm when the gust is at 10° on the horizontal angled sails. This sounds a lot, but is well below the ultimate strength of the stock itself assuming it was in good condition. The stocks at Ibstone and Bocking must have been in quite a bad state for this to have broken them. At Ibstone, there were no clamps in place, which not only give additional strength, but also prevent complete collapse, saving both the sail itself and people on the ground.
Sail Turning
There is no sail rotating torque on the sails revealed by this analysis, and I have to take into account the wind gradient from the ground upwards in order to explain why the sails turned so violently. The wind gradient results in the forces applied to the lower sails being significantly less than the upper ones. This in turn means that side forces are unequal above and below the wind shaft, and create a turning torque on the sails in both directions depending on the gust direction. Applying this, for Impington, the maximum turning torque is about 5 Tm when the sails are at 45° and the gust offset is at 15°. Notice that this torque occurs independently of any torque caused by the twist in the sails.
The RSJ sprag at Downfield was placed at about 1 m from the centre, so this is the force that would have been bending it. I am surprised by this result, but still feel that it is not enough to bend the beam itself. I think it more likely that, with the one-way sprag, the sails first turned backwards and then gathered momentum going forwards before impacting the beam with the clasp arm. The brake wheel will not withstand these forces.
Recommendations
Surprising and surprisingly large wind forces can arise from the effects of gusts in storms. Here are some recommendations coming out of this analysis.
It’s obvious that the absence of the fan tail at both Heckington and Burgh le Marsh was the primary cause of the accidental onset of winding, and meant that, once winding was initiated, there was nothing to stop it continuing until the sails had turned far enough to reverse the shutters. Even a moderate tail breeze will reverse shutters on both Impington and Burwell mills, buckling the push rods. Once this happens, the drag and lift forces multiply dramatically, and will both continue to wind the mill and eventually to take the cap off. * It is quite apparent from the above that, if it is absolutely necessary to remove the fantail for maintenance, then the sail shutters must also be removed.
For fantail maintenance such as changing blades or stocks,* remove and replace symmetrical pairs, leaving the rest of the fan in action the whole time.
The Bocking and Ibstone sail losses resulted fundamentally from weakness in the stocks, which should have been inspected regularly and which would have been more secure with clamps - less damaging to the sails and less dangerous had the stocks still broken.* If your stocks are doubtful, remove the shutters even if you can’t do anything else.
- Put clamps on your stocks
From both of these events, the overwhelming conclusion must be that* removing shutters when the functionality of the mill is compromised will save you a lot of money and reduce the risk to people.
The turning tendency at Downfield in both directions can easily be seen even on a well locked mill. It is possible that a further piece of advice by Chris Wilson may be valuable: he always leaves his sails “idling” with the shutters open and the brake off during storms. This may reduce all the forces on the mill, and I intend to investigate this much debated question in the future. However, if you prefer to prevent the sails from turning* make sure your sails are secured equally in both directions. Do not rely on the brake.
Acknowledgements
The wind data came from the SPAB’s anemometer
Luke Bonwick supplied details of the various mills
Jim Bailey gave details of Heckington’s tail winding event
The Aerofoil lift and drag coefficients came from Sandia National Labs report SAND80-2114
The Picture of Vortices over the Indian Ocean came from the NASA / GSFC / Jeff Schmaltz / MODIS Land Rapid Response Team
