◼️ Tom⇒maths: Maths in Museums: Roaring Meg

Maths in Museums: Roaring Meg

Goodrich Castle, a ten-minute drive from the Welsh border in Herefordshire, England, has to be one of my favourites^[1]. It's a Norman medieval ruin that played host to an English Civil War siege by Parliamentary forces upon the Royalist forces stationed there. Despite not having its defences updated to 17th-century standards, the medieval castle stood up well to direct attacks and artillery was introduced to the conflict, with Parliamentary Army Colonel John Birch commissioning the casting of a mortar called Roaring Meg.

A short-barrelled cannon with a 390mm diameter rests in a wooden, wheel-less gun carriage. It is photographed here in its position on a tiled outside floor, with parts of ancient stone walls visible in the background.

Situated amongst the ruins at the modern day English Heritage site, the Civil War's only surviving mortar, Roaring Meg, is accompanied by an explanatory panel, which is shown in the photograph below. The focus of this post is not the story or the text, but the main image included in this panel. It shows a drawing of a mortar similar to Roaring Meg, with a trail of smoke arcing from the muzzle of the cannon to the landing position of a spherical projectile just in front of a castle. Around the base of the mortar are other projectiles, presumably waiting to be fired, and a caption underneath the arc of smoke reads "A Morter Shooting upon a Castle". At the mouth of the gun floats a quadrant; a sort of 90-degree protractor with a plumbline hanging down from the join that forms its right-angle, marking off an angle on the scale that curves between its two arms.

Photograph of a panel accompanying the Roaring Meg mortar at Goodrich Castle. The main body of text explains its use by parliamentarian soldiers to besiege Goodrich castle, but our focus here is of the image which is described in the blog post.

Roaring Meg's explanatory panel, created by English Heritage, photographed by me.

I was intrigued by this image, and a reverse image search suggests that it's the top half of a page from Thomas Venn's Military & Maritine Discipline in Three Books, specifically the third of these, The Compleat Gunner. I've included the full page as an image below, but it can also be explored (along with the rest of the books) at the Internet Archive. The bottom half of the page is a diagram showing another view of the mortar with the quadrant floating over its muzzle again, and a series of lines beginning at the muzzle and radiating out at different angles, labelled A-O. Each line can be followed until it curves, then continues in a straight line ending at the landing point of one of thirteen mortar projectiles which have been fired from the mortar at an angle indicated by the letters.

Image obtained from an auction listing for the book at Bonhams.

This diagram is captioned "How you are to use the quadrant afore described for a Morter, as you may see by the falling of the Granado uppon the Letters,". Most of the landing points have two projectiles (Granado), demonstrating that there are two angles which can be used to reach each landing point: one shallow, one steep. Most, that is, apart from the furthest possible landing point, which only has one way to reach it.

The diagram doesn't provide specific angles, but it does do a great job of showing that (1) changing the firing angle changes the distance that the projectile travels, (2) that the furthest possible distance is achieved by firing with the mortar set to a specific sweet-spot angle, and (3) that for all other achievable distances, there is a pair of angles, one greater than this sweet-spot angle, and one smaller than it, that will put the projectile in the same place.

This one object, its story, and accompanying historical commentary and diagrams, has potential for a range of mathematical explorations with a variety of cross-curricular links, from hands-on experimentation (they sold wooden make-your-own-mortar kits in the shop) aimed at primary-age students, to opportunities for A-level students learning about mechanics to have a go at modelling scenarios algebraically, and then testing their models.

As always, if you'd like more museums and galleries (including Goodrich Castle, and English Heritage in general) to bring their mathematical stories to the surface, then consider letting them know when you provide feedback after a visit: organisations in the cultural sector really care about visitor feedback, and the only reason that most of them don't do anything to help you play with maths while you're there is that they don't know you want them to.

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Footnotes

I love a castle - even the ones that are just earthworks with nothing much to see - but for a relatively small site, Goodrich has it all: for a ruin it has a lot of walls and multiple levels to explore, including the (now dry) moat, a pitch-dark dungeon, and a tight spiral staircase that you can use to see breathtaking views from the top of the keep. They also had some stuff out in the courtyard to play with - quoits and the like - and there's the obligatory shop and cafe. [back]