Yurt Calculator
Yurt Notes & Calculator *
written by Rene K. Mueller, Copyright (c) 2005, 2006, 2008, last updated Sun, September 22, 2013
The height h is 140-180cm, or even 200cm, smaller yurts (e.g. 3-4m) are lower, e.g. 6m often is 1.60 or more.
The height is so low because the resulting room is better to heat, but for reason of comfort you may choose
to have it your head height high.

Traditional yurt development comes from a given w khana-spacing and length of a khana-section, and
then the amount of poles is calculated, e.g. 2-3 khana sections, or 4-6 khana sections for
large yurt, then the poles are counted. I have prefered to define the yurt from the amount of poles for reasons of angle 
measurement and symmetry (e.g. multiple of 4 poles), to increase or decrease npoles 
in order to make and see how large the spacing of w gets.
The resulting w should be between 20-35cm in order to create a stable 
wall / khana, good stable laths may allow larger spacings of w.

Usually the roof poles lie on each lath junctions, which is arranged as crossed lattice.
Modern yurts disregard this approach and lie the roof poles on the rope which holds
the wall / khana together, this way one is very flexible to build with given parts 
(e.g. wall / khana, crown-wheel / toono etc) multiple sized yurts, but you
sacrifice some of the stability of the lattice wall.

Traditionally and also for stability the wall lattice is spread so the crossing laths
relate in 90° (αkhana) angle, but you may have a shorter angle like 60-80° and
have with shorter laths a higher wall.

The diameter of the crown-wheel / toono is traditionally 20% of the yurt diameter, but this is just a reference nothing more.

Yurt Geometry Sketch (Human is 170cm/5'7")

Edit the numbers in the yellow fields, and then press "calculate" button.


d = cm, 
h = cm,
npoles = ,
dwheel = cm

height defined by htot = cm, or via

αroof = °, (0..50°)


Metric vs English System
As wood and other material is in the US still in feet and inches measured, may this small calculator assist you.

 cm = 
 ft
Enter your number, and hit ENTER or TAB


1 yard = 91.44cm, 1' or feet = 30.48cm, 1" or inch = 2.54cm. 1cm = 0.01m, 100cm = 1m




Hint: The larger the d diameter, the more poles you need, try a multiple of 4 for the roof pools (npoles). The resulting w should be between 20-35cm as mentioned to get a stable khana (e.g. diameter cm / 10 = poles gives w = 31cm).

Also, wwheel shouldn't be too small in order to assemble the roof poles on the roof/crown wheel, increase the roof/crown wheel diameter dwheel if necessary. Also, αkhana you can alter, and increase h by a given lkhana (e.g. 2m lkhana with 90° gives h ~ 142cm, but with 83° you reach h ~ 150cm).



General:

total circumference c = m,

floor area Afloor = m2

total volume Vtotal = m3


Wall / Khana:

spacing of roof poles & khana w = cm,

length of khana lath lkhana = cm,

spacing between holes wkhana-holes = cm,

total  holes (extra cm left),
with αkhana = ° angle(if you change it,  again)

total of apprx. nlaths =  khana laths required,

gives nkhana-sections =  khana-sections,
when lkhana section = m(if you change it,  again).

Roof Poles / Uni:

Roof pole length lpole = cm,(add additional length for entering the crown-wheel / toono 3-4cm and the other end with cord 2-3cm, total e.g. 6cm)

angle between each pole αpoles = °,

space between poles at the roof/crown wheel wwheel = cm



The canvas has two main pieces: the roof, and the wall.

Roof Canvas, Lanewise
Roof Canvas

In order to calculate the angle αcutoff I simply calculate both circumferences, based on droof and d, and then substract the later from the first, this is the length which is left and needs to be cut away:

αcutoff = (droof * π - d * π) * 360 / (droof * π)

    wcutoff = sin(αcutoff/2) * lroof * 2

Therefore 

lroof = cm,

droof = cm,

αcutoff =  °,

wcutoff = cm


Aroof = m2 e.g. square canvas of m, apprx.m2 left over. 

Lanewise

Use multiple lanes (common way to get canvas) as indicated to compose the shape:

nroof lanes = droof / wlane (and round up)

ltot lanes = droof * nroof lanes

You can calculate more exact (approximate the circle without tilt cutoff αcutoff):

wlane cm,
wroofextra cm,


whereas last lane has
m left over.

Total length as one lane: m

Often canvas comes 1m - 2m (e.g. 1.60m) width, but can be hundreds of meter long. I recommend for the height of the yurt h not to go over the common 1.60m, e.g. I choose 1.50m so I have 2 times 5cm left top and bottom for the seam.

Note: You need to add extra length as you have to sew the roof canvas (enter 5-10cm less than the actual lane width for wlane), and also fold its seam two or four times, additionally, bought canvas usually shrinks 5-7%, so buy preshrinked canvas or shrink it (means wash it) before you cut.

Sewing: Either  mark the middle line of each cut canvas lane (in the illustration the red line), and then align the lanes along this middle line or calculate the offset of each next layer to the previous; maybe also use needles to attach the next lane to sew, avoid wrinkles, with some practice with a sewing-machine you might do it without needles. 

When working from top to bottom, next lane over previous lane, until you reach the center, then next lane under previous lane. For the rain cover you might use one big piece of canvas, instead to lay lanes to each other and leave a lot of seams where water can leak through.

 Canvas Layout
In the real world application, you might not cut αcutoff away but just make a line cut, and let the two laps overlap each other, in this case you need an additional layer of cover, or bind it with a cord. 

For the rain insulation I use a square blanket of synthetic and leave it in that shape and make no cut at all but fold it for the tilt and tie it with 4 or 6 cords to the bottom of the yurt. 

The cotton interior roof canvas I compose with multiple canvas lanes, and for a roof angle αroof of 25° I let the canvas leave without cut or folding the spare, the canvas did hang a bit between each roof pole. For larger roof angles you may consider to truncate the canvas to fit it more closely.


Roof Canvas, Lanewise Traditional
Traditional Lanewise

Traditional roof canvas is sewed lane wise, e.g. you attach various lanes until you reach the center, that part of the canvas is laid unto the yurt skeleton, and the next lanes are individually matched to that form and step by step added. It's a time consuming procedure, and the roof canvas fits closely but becomes more inflexible. As I mentioned before,
for 25° roof angle a flat circle formed canvas is sufficient, the extra canvas (vs cone) is distributed evenly among all the roof and hangs a bit (1-2cm) down between the roof poles.


Roof Canvas, Pieslice-wise
Pieslice-wise

If the roof is small enough and match the width of the canvas, or the canvas available makes it more suitable, you can also make it pieslice-wise and arrange the pieces so it fits the lane nicely, with little leftover. 


slices
   

couter =
cm

cinner =
cm

lpole = lpie =
cm, and add 10-15cm (wroofextra) to have it overlap to the wall


The pieslice-wise approach can be used for inner but also outer rain canvas, yet in case a 100% leak-free seam is then required, and since the seams run top to bottom of the roof and not sidewise this is doable. I use the pieslice-wise approach for the thermal insulation layer.


As you see, for each individual layer (rain canvas, insulation, and interior) you can use the calculator. I use for
 rain cover: one piece of canvas of PE (droof x droof); roof: longlivity 12-18 months, wall: longlivity: 24-28 months
 thermal insulation: lanewise bubblewrap; roof: lasts 12 months max if exposed to UV by the sun
 thermal insulation: piewise, straw filled blankets
 interior cotton: lanewise

Wall Canvas

Wall Canvas Section with cords to bind
This is rather simple, it's rectangular, and c (circumference) times h of the lattice wall / khana. With your numbers, the wall canvas is m or 
Awall = m2. 

Best you choose wlane the same as h, then you can use one lane for the entire wall canvas; otherwise you require to sew lot's of vertical lanes together to achieve h, with your 
wlane you do  for the entire wall canvas.

You may substract the door width (discussed later in more detail), but I recommend you plan with extra length, it's easier to cut than add more canvas later. I used 10m long sections, attached short cords in order to bind it to the main rope, you can also bind to the roof-poles.

Total Canvas

Total canvas of apprx. m


You can get an approximate cost overview, choose your own currency (US$, €, CHF etc).


Cost per canvas meter: 
total cost canvas: 

Cost per roof pole: 
total cost roof poles: 

Cost per khana lath: 
total cost khana: 



Total Cost Canvas/Poles/Khana: 


You still need:
 crown wheel aka toono
 door aka khaalga
 multiple layers (e.g. interior, insulation layer)
 floor

Often the canvas may the most expensive part of your yurt so it makes sense to really get a good and priceworthy source for the cotton, the same for the raincover. 

My 6.4m diameter yurt with 64 poles did cost apprx. CHF 1000 or US$ 800 or € 670 (bamboo poles for roof & wall, PE as rain cover, wholesale cotton 1.5m wide etc), see details in my yurt diary.
