Calculator for yurt component dimensions and count. Specify a diameter and a wall height (or use the defaults) and you'll be shown how many poles, and of what lengths, are needed.

yurt.js

const defaults = {
  units: 'ft',        // units to use, could be 'ft' or 'm'
  diameter: 14,         // units
  wallHeight: 6,        // units, at outer edge
  khanaHoleSpacing: 1,  // units, spacing between crossing rods
  roofAngle: 25,        // degrees from horizontal
  tonoDiameter: 1,      // units
}

function deg2rad(deg) {
  return deg * (Math.PI / 180);
}

function calculateCircumference({diameter}) {
  return Math.PI * diameter;
}

function calculateUniRadius({diameter, tonoDiameter}) {  
  return (diameter - tonoDiameter) / 2;
}

function calculateUniLength({roofAngle, ...options}) {
  return calculateUniRadius(options) / Math.cos(deg2rad(roofAngle));
}

function calculateRoofHeight({roofAngle, ...options}) {
  return Math.sin(deg2rad(roofAngle)) * calculateUniLength({roofAngle, ...options});
}

function calculateKhanaRodLength({wallHeight}) {
  // Assuming 45 degrees, length is the hypotenuse
  // of a right-angled triangle with sides of the desired wall height.
  return Math.sqrt((wallHeight*wallHeight) * 2);
}

function calculateKhanaRodCount({khanaHoleSpacing, wallHeight, ...options}) {
  // A minimal lattice has just two holes - one at either end
  // Thus, for each length of the khana rod around the circumference, there are 2 rods
  const wholeRodsInCircumference = calculateCircumference(options) / wallHeight;
  
  // A denser (thus stronger) lattice has more holes and one rod per hole.
  // The rod length divided by the hole spacing gives the number of holes.
  const holesPerKhanaRod = calculateKhanaRodLength({wallHeight}) / khanaHoleSpacing;
  
  return wholeRodsInCircumference * holesPerKhanaRod;
}

function buildYurt(options = {}) {
  // Find any missing options and their default values
  const missingOpts = Object.keys(defaults)
    .filter(key => !(key in options))
    .reduce((obj, key) => {
      obj[key] = defaults[key];
      return obj;
    }, {});
    
  // Then mutate the options object to include defaults
  options = Object.assign(options, missingOpts);
  
  // Compute some re-usable values
  const roofHeight =  calculateRoofHeight(options);
  const khanaRodCount = Math.ceil(calculateKhanaRodCount(options));
  const uniRodCount = Math.ceil(khanaRodCount / 2);
  
  // Build up an object specifying the yurt
  return {
    units: options.units,
    diameter: options.diameter,
    height: options.wallHeight + roofHeight,
    roof: {
      height: roofHeight,
      angle: options.roofAngle,
      uni: {
        length: calculateUniLength(options),
        count: uniRodCount,
      },
      tono: {
        diameter: options.tonoDiameter,
        holeSpacing: options.tonoDiameter / uniRodCount,
      }
    },
    walls: {
      circumference: calculateCircumference(options),
      height: options.wallHeight,
      khana: {
        length: calculateKhanaRodLength(options),
        holeSpacing: options.khanaHoleSpacing,
        count: khanaRodCount,
      }
    }
  };
}

const yurt = buildYurt();
console.log(yurt);
console.log();

console.log(`YURT`);
console.log(`----`);
console.log();
console.log(`Diameter: ${yurt.diameter.toFixed(2)} ${yurt.units}`);
console.log(`Height: ${yurt.height.toFixed(2)} ${yurt.units}`);
console.log();
console.log(`To build this yurt you will need:`);
console.log();
console.log(`- ${yurt.walls.khana.count}x ${yurt.walls.khana.length.toFixed(2)} ${yurt.units} khana (lattice) poles`);
console.log(`- ${yurt.roof.uni.count}x ${yurt.roof.uni.length.toFixed(2)} ${yurt.units} uni (roof) poles`);
console.log(`- 1x ${yurt.roof.tono.diameter.toFixed(2)} ${yurt.units} diameter tono (crown) with ${yurt.roof.uni.count} holes spaced every ${yurt.roof.tono.holeSpacing.toFixed(2)} ${yurt.units}`);