When I started a PhD on golf-green ball impacts back in 1985, my supervisor Dr Alastair Cochran suggested that I look for information on the Dambusters. For those of you not old enough to have seen the 1955 film starring Michael Redgrave, the Dambusters were the RAF’s 617 Squadron who flew Lancaster bombers during the 2nd World War. In Operation Chastise, they flew deep into Germany on a fully moonlit night to drop bouncing bombs onto reservoirs in an attempt to burst their dams and flood the factories in the flood plain below.
Now just what was the connection with golf? It wasn’t that Alastair was a 2nd World War buff (I don’t think), but he remembered that Barnes Wallis’ innovative design required the pilots to fly the bombers just above the water and drop spinning cylinders packed full of explosives. The key was that Wallis optimized the speed, angle and back-spin of the bomb’s bounces, so that it came to a halt at the dam and rolled down the inside of the wall before exploding at a depth of about 10 m.
Alastair reckoned that I might find something about Barnes Wallis’ testing that would shed light on the mysteries of golf balls landing on golf greens (the topic of my now ancient thesis). Back in the 1980s, the internet was only just about to happen and finding information was a slow process. Literature searches were done with microfiches and card files and lost in the intricacies of rigid-plastic half-spaces, I forgot about the Dambusters.
Until the other day that is. During a lunchtime literature search using Web of Science (coming up with more papers in the flick of a mouse than a 1980s day in the library) I came across a paper on the impact of spinning spheres on water by Truscott and Techet. The abstract described the creation of ‘wedges of water’ and determined the lift and drag of the sphere after impact. Despite trouble accessing the full paper, my interest in Barnes Wallis bouncing bomb – nicknamed ‘Upkeep’ – was re-kindled. A quick search took me to the UK National Archives and the RAF Museum which provided more than I needed.
Figure 2. Original footage of the bouncing bomb tests carried out by Barnes Wallis and his team.
The full scale experiments carried out by Wallis and the aircrews are frightening to see – twin-engined Mosquitos or Lancaster Bombers carrying out experiments with seriously large spinning cylinders, sometimes fatally. Their experiments showed that the optimum impact of the 4,200 kg cylindrical bomb was around 100 m/s (225 mph) at 7° to the water with about 8 revolutions per second of backspin.
In spinning impacts, researchers tend to use the spin-ratio (ωr/v) to characterize the impact where ω is the spin, r the radius and v the tangential velocity of the object in question. With a diameter of around 1.3 m, this gives a spin ratio for Upkeep of about -2.1 (the minus sign indicates backspin).
And guess what? Alastair was right – the bomb bounces just like a golf ball (Figure 4). I’ve guessed the rebound value for Upkeep from film footage so take it lightly for the moment but the cylindrical bomb seemed to retain backspin for all bounces indicating that the rebound spin ratio was always negative. Heavily lofted golf shots such as a 9-iron or a pitching wedge can have backspins as high as 160 revolutions per second (about 10,000 rpm), landing with large negative spin parameters and bounce in much the same way. With shots onto links golf greens the backspin slows the ball on the first bounces before the spin ‘engages’ later and the ball screws back along the green.
So, next time your pitch onto the green bounces into the rough because you didn’t get the spin quite right, just remember that sport isn’t, as the saying goes, about life or death. The bomb that Barnes Wallis developed for the German dam raids of 1943 was one of a number of spinning bombs that he was working on for attacking boats, submarines, bridges and the like. One had the name highball but Wallis had a generic name for all of them. Guess what it was? The Golf Mine.
Watch this last video and you’ll see how Wallis might have got his inspiration.
Figure 5. Barnes Wallis theories in action.