Hexagonal tent design model
This post discusses an efficient and effective hexagonal tent design (hexamid) that can be scaled to any size, according to fabric width or ten sizing requirements using a spreadsheet model.
I have been inspired by Darren’s FTR tent design (Shit Talk 2021) and I have posted on the loadbearing tent stove pipe element of the design. An additional comprehensive series of photographs of the FTR tent and stove have been posted to understand and share the wonderful hexagonal tent design with others. This post takes a closer look at the FTR tent design and the critical dimensions of the fabric panels and includes a mathematical model that can scale Darren’s tent to any size for terrestrial or snow pitching with or without a tent stove, (loadbearing or otherwise).
Being a long term fan of pyramid bell tents, of up to twelve sides and more recently square ones, I intend to make experimental hexagonal tents according to Darren’s design. My tents will also be made with polyester umbrella fabric that I have described in a post about an Experimental breathing polyester tent. “Luckily, I have an abundant supply for such experimentation.”
This polyester fabric reduces several problems including wet stretching and the ‘dreaded condensation problem’ that is associated with the wonderful silnylon fabrics that are so popular these days. The polyester will have very different stretch characteristics to Darren’s silnylon FTR fabric.
I thought that making a spreadsheet model of the hexagonal tent design would be good for me to better understand Darren’s design and make it scaleable. This would allow me to plan a tent of any size, match the dimensions to my requirement, and cut it efficiently from my available fabric. It should help to make small-scale models to test before committing the project of making the real tent. I also have a vague idea of making a mega tent that can be comfortably shared by several people on snow skiing trips to save weight by efficient sharing.
Such a model may be of interest to others who are passionate about making their own tents either for camping on deep snow or terra firma?
Exploring the hexagonal tent design
My starting point for the models was the dimensions kindly set to me by Darren on a sketch. I played with a paper pattern that was made approximately to scale according to those dimensions.
It dawned on me that the design could be approximated by or thought of as six panels of equal isosceles that are made or formed as symmetrical pairs that share a common straight grain. These three panels are then sewn together along their bias-cut edges and extra smaller triangles of fabric are added to make the canopy reach the ground.
The three largest tent panels can be simply cut from a wide roll of fabric or a strip of fabric (‘from the roll’) with an additional strip added to it to meet the requirements of the tent size (As shown in the featured image).
Then six additional smaller triangles of fabric are added to complete the formation of an inverted kite shape that has an axis of symmetry down through the straight grain, forming two equal isosceles triangles on either side. The two panels could also be cut separately and sewn together for some situations where this may make a more ‘economical cut’ of the available fabric (More on this later).
The three tent panels are cut with bias grain on the outer edges (A) where they will be sewn together to form three primary tent ridges that will stretch when the tent is pitched.
The three secondary tent ridges are formed along the straight grain of the kite shape (A+D) with two triangular panels sewn on to complete the two isosceles triangle shapes. These ridgelines are where the tent doorway zipper/s are attached.
The bias cut edges (E) become the hemmed contact with the ground and the attachment line for a snow or bug skirt. (Later, for one particular design option, I discuss the possibility of extending the triangle to form snow/bug skirts.)
The FTR tent dimensions to make the pyramid tent design model
From the dimensions sent to me, I calculated that the long bias grain seam line (C) was about 105.5″ which is about 2.5″ shorter than the straight grain ridgeline. “Darren confirmed that it was a good old 9′ or 108″ on the straight grain, in real man measurements!” So they are not perfect isosceles triangles. “However, I think they behave perfectly like them when differentially stretched.
I think that Darren determined the length (D) after such stretching, as can be imagined from the photo below. I think this difference will, in part, allow for the greater stretching that will occur in the bias grain seam. “It is quite likely that any remaining difference in the pitched ridge lengths is no big deal anyway.”
Dimension definitions for the hexagonal tent design
As explained above I could not quite reconcile all the dimensions provided, so I settle on using just two (A) and (B) that allowed me to calculate the isosceles triangle APEX ANGLE and all the remainder of the dimensions (C) to (H). Then I assumed that all the six triangles were true isosceles.
In my spreadsheet model, I have used the following terms to define each dimension:
Note: The length values can be entered as inches or centimetres (or even cubits!) and the outputs will be of the same units as the input. Blocks of calculators below each model also convert between inches and cm and vice versa if required.
(X) APEX ANGLE The design models assume there is a constant tent apex angle for each of the six panels. The starting point is Darren’s FTR tent angle which provides a moderate tent slope. “He assures me that it sheds snow quite well.” I have calculated this angle from the (A) and (B) dimensions that he supplied: X= ATAN (opp/ajd)=ATAN (B/A)=ATAN(70/79)= 0.725068778 Radian or 41.54 Degree.
Note: “I grew up with trig angles expressed in degrees. You know the old favourites 1, 30, 270 degrees etc. They have a real meaning directly in my brain, but if I said 0.017453286, 0.523598588, 4.712387295 radians, most of us would not have a clue.” Consequently, I have used radians in the model for their use in trigonometry functions in the spreadsheet and also converted them to degrees for our brains to also comprehend. “I think this is in line with Darren’s design philosophy of keeping the human dimension in the design.”
The X angle can be reduced to make the pyramid steeper or taller (e.g. for snow shedding or head clearance with firm ground pitching where snow excavation is not possible). Alternatively, it can be increased (within limits) to make it flatter where head height can be maintained by snow excavation or you are happy to crawl into a tent instead of walking! “Both Darren and I like walk-in tents.” Lastly, in one model I take X an obtuse angle to improve the fabric use efficiency (excuse the pun). This is discussed later if you get that far without nodding off.”.
(A) ROLL WIDTH. This is the top straight grain drop length of the three kite shapes. It could be the width of the fabric roll or the width of the roll with an extra strip added (as shown in the above photos). This length will have EXTRA straight grain triangles of fabric added to complete the ridge to make its length equivalent to the bias cut RIDGE length when stretched (give or take, according to the stretch of the bias-grain ridge).
(B) WIDTH. Horizontal straight grain length of each of the six tent panels.
(C) RIDGE. Length of the isosceles triangle sides that form the bias-grain ridges and also the straight-grain ridges. “These may need to be changed a little to accommodate the differential stretch of the two ridge type, but there again, the tent may pitch well without any such adjustment.”
(D) EXTRA straight grain drop. This is the extra straight grain length of the smaller composite triangles that extends the top drop length to make it equal RIDGE.
(E) HEM. The bottom length of each of the six tent panels. It also is the length of radius through polygonal base points.
(F) HEIGHT. The vertical distance between the ground and the tent apex.
(G) DIAMETER. The diameter of the tent where six ridges would touch the ground (HEM*2).
(H) USABLE diameter. The diameter of a pyramid tent is limited by the clearance of the tent canopy from the ground (when not pitched over a snow pit). I have set this clearance value at 30cm or 11.81″ considering that this clearance is needed for sleeping positions that will not be in contact with the tent canopy. Then I have calculated the diameter of the tent footprint that meets this clearance criterion. It should help to better evaluate the tent sleeping capacity.
(I) USABLE square. When camping, sleeping positions occupy the approximately rectangular shapes of our sleeping mats. Consequently, efficient multiple positions will often add up to a rectangular shape, so I thought it would be good to calculate the size of the square that fits inside a circle of the USABLE diameter.
The hexagonal tent design spreadsheet model
My trigonometry and Pythagorean theory were a bit rusty, but it all came back once I came to grips with some of some modern terminology used in spreadsheets. My apologies to those who may have found a simpler or more elegant way of solving the triangulation.
Eventually, I found that I could calculate all the dimensions and the critical APEX ANGLE from the model by using only two primary inputs. I chose to use APEX ANGLE and ROLL WIDTH, partly because that is what I started with, and also because they are simple and straightforward parameters to hold in the designer’s mind without the complexity of mind-warping stretching.
I did make models that used other pairs of input such as TENT HEIGHT and TENT DIAMETER, but it started to get a bit complex. If a designer wishes to focus on this pair of parameters the above model can easily be used to juggle APEX ANGLE and ROLL WIDTH to determine these within the constraints of the FTR design and the resultant model (as discussed later).
Note: The image below is not an active spreadsheet, so please see the comment below if you would like a copy of it to play with.
The sample models below show the prediction of seven sets of tents design measurements according to different inputs.
Navigating within the hexagonal tent design model/s
The structure of the models is that the first column (grey fill colour) is the FTR tent specifications. “Look by all means to see if my maths and trig is correct, but don’t edit these cells. They should be left alone! “ The adjacent six columns contain identical models that use the same calculations. The two yellow cells are for inputs and the blue ones are the new corresponding outputs.
The user can play with changing the yellow cells to see what happens to the blue ones. Any of the model columns can be copied to create more models if required. If you want to model in imperial units, use an ‘inch’ one to copy from. Similarly, use a ‘cm’ model to copy for metric modelling.
The values in these grey cells, apart from the two inputted values, are all calculated within the model and provide validation of the correct calculation that I have created within the model by returning the original FTR specifications as supplied by Darren.
Note: I have added a supplementary calculator to the bottom of each model to make further estimates of tent parameters and convert between imperial and metric units. They are colour coded orange and lime green. “I have labelled them this way for those people who have eyes that do not see the full spectrum of pigments of the imaginations of others.”
The orange cells are to convert inches to centimetres and the lime cells are to convert from centimetres to inches. They also calculate the fabric area and the yellow cells can be used to enter an alternative fabric gram/square meter (gsm) to calculate the total tent fabric weight. These cells can be copied below any new models that you may make. They are not integral to the model calculations.
Examples of use of the models to balance the human scale and fabric use
The model is good for generally estimating the size of a tent and will quickly define the size of a tent that can be made efficiently from particular fabric ROLL WIDTHS. It could help designers make better fabric choices during the design phase.
I will use my polyester fabric that is 150cm wide as an example. It is on the ‘heavy-side’ (58gsm), but I hope that this will compensate for any lack of strength when compared to lighter nylon fabrics that are now very popular and apparently adequately strong.
Model 6 shows that an FTR tent could be simply made with the three major triangles cut from the full 150cm roll width. It would have a generous 284cm diameter and a rather cramped 141cm height. “Certainly not walk-in comfort that both Darren and myself appreciate when snow camping.” However, it may be suitable for snow camping where snow excavation can easily provide that extra height for comfort. With 58 gsm fabric, the tent fabric would weigh 460g. This would make it a nice lightweight tent for one or two with a tent stove.
Model 7 shows a tent that can be made by adding an extra 20cm to the fabric width. The height is still not ‘walk in’ for non-snow use.
Adding 50cm, Model 8, shows the tent can reach walk-in height (188cm or 74″), It will be ‘stooping if you are tall” and a diameter of 379cm or 149″. If the APEX ANGLE is increased to 45 degrees, Model 9, the tent it is still walk-in for the vertically challenged (72″) but it can have a simpler and more economical fabric layout (as described later). “These two tents reach the size of Darren’s FTR tent and it should be no surprise as the 200cm fabric width is equivalent to the Darren’s 77″ fabric width that we started the model with. Also, the tent fabric weights are between 824 and 984g which is similar to the FTR weighting the same fabric (829g).”
In Model 10 adding 75cm (half a ROLL WIDTH) would make a very efficient design (If you don’t like left-over scraps). It takes the tent to full walk-in height (83″, even for basketball players who go skiing). Again, changing the angle to 45 degrees, Model 11, reduces the height to 81″ but can make fabric use very efficient (as discussed below).
Obtuse tinkering with APEX ANGLE and efficiency of ‘fabric use’
I have become accustomed to very efficient use of fabric with my four-sided pyramid tents. “Most angle cuts leave a perfectly useable part on the other side of the cut.” So I was somewhat frustrated when I laid out the shapes of the FTR and found that the three major triangles, left two wasteful half triangles as scrap. “I think this is a unique problem for what is basically a three-sided tent design that masquerades as a six-sided tent.”
Also, for the six lesser triangles I would need to cut eight to get six of the right shape. “Some might call me a tightarse but I do like efficiency and like to avoid waste. After all, that is what the world needs right now!”
Consequently, as I tinkered with both the mathematical model and the paper one, it became apparent that the connected tent panels when laid flat covered nearly 270 Degrees. “That is a magical geometric angle for a three-sided object. “You would never recognise it if you were only thinking in Radians!”
The use of a 45 degree (270/6) would increase the FTR APEX ANGLE by only 3.5 Degrees. The magic of this small change (Model 5, 9 and 11) makes the three largest tent triangles become simple right-angle isosceles triangles. In short (A)=(B). This means that two large triangles can be cut efficiently, leaving two half triangles at either end. These could be joined together to form the third triangle, forming the ridge with a zipper in it.
Addition of snow/bug skirts
Because the smaller triangles can be cut directly from the ROLL WIDTH it also means that fabric for the snow/bug skirts can be simply allowed for while cutting these triangles. This will save their subsequent sewing to the HEM. Such bias-cut skirts will stretch in sympathy with the HEM fabric and I expect will allow a better tent pitch than with straight grain equivalents.
[Add sketch of base triangle layout with skirt allowance included]
Discussion & conclusion about the hexagonal tent design model
The model appears to work well as the values returned by the model are very close to Darren’s original FTR tent panel measurements (as supplied to me). They should be able to accurately determine the measurement for any scaled tent of any size, from small scale model testing tents to mega tents.
Effect of seam stretching
The effect of differential stretching of the bias-grain and straight-grain ridgelines will need to be evaluated by experience. However, I expect that it will not be an issue that will prevent a good tent pitch. The FTR tent had a straight-grain ridge of 106″ which was only 2.5 longer than the bias-grain ridge that would have greater stretch (104″ without stretching). I doubt that this small difference would have fully compensated for the differential stretch. If any compensation was needed, it could easily be done by extending the straight-grain hemline after the primary tent panels were sewn together and pitch tested.
Catenary finish to the bias cut seams
Catenary seaming of the bias-grain seams seems to be a way of improving the pitch of such stretchy grain seams. The cat-line should be able to be determined after using basting stitching to attach the three bias-grain seams together. The catenary curve can be estimated by the temporary pitching of the tent and performing the ‘thumb and forefinger pinch test’ to find the catenary line. “You probably have your favourite way of doing cat-curves.”
The 45 degree FTR and the human dimension in the hexagonal tent design
Darren correctly puts particular emphasis on tent dimensions regarding the comfortable walk-in access and room for multiple standing or sleeping people with a cooking/heating device deployed in the centre of a tent. He even provides three doorway zippers so there is no excuse for stepping on anyone else’s sleeping bag. “My tent philosophy is very similar, but I use the centre of the tent as the corridor and only have one doorway and seldom resort to the use of an ice axe to maintain tent decorum.”
I think this 45-degree design might make a good alternative, providing it has enough roof slope to shed snow effectively. I was interested (or relieved) to see that Model 9 resulted in similar tent dimensions to the original FTR tent.
[Add a photo of my scale model and full-scale FTR tent when I make them.]
Access to the spreadsheet models
I could not find a way of embedding the working spreadsheet in this post. I would be happy to send the working spreadsheet by email to anyone who is interested in tinkering with it. Please use my contact form or use the comment section below for this purpose.
I have already found and corrected some little errors since posting so I would welcome feedback about the models and would like to know if you find any errors that need correction.
Tim
OTHER POST FOR PYRAMID TENT FANS
DIY Breathing polyester tent for backpacking
DIY breathing polyester tent for backpacking- Beat the dreaded condensation problem
Polyester ageing- About as interesting as paint drying
DIY silicone seam sealer- Getting a long pot-life
Tie out tabs for pyramid tents- Keeping DIY tabs cheap, small, simple, strong and light
A pyramid tent vestibule- Turn a pyramid into a winter palace, using a spreadsheet model
