Fuel Tank Measuring Stick Calibration

tank-volume.py

#!/usr/bin/env python
# Computes the volume of a fuel tank as a function of height from the bottom.
# The computation is intended to support creating a dipstick to measure
# fuel remaining as a function of fuel depth obtained from the dipstick.
# Tank shape is assumed to be the common one where the cross section is
# composed of a semicircle on the top and bottom separated by a rectangular
# region of arbitrary size.
# The input to the script are tank measurements length, width, and height
# in inches.

from math import acos, pi, sqrt
from os.path import basename
import sys

"""Gallons per cubic inch"""
GAL_PER_CI = 0.004329

"""Liters per cubic inch"""
L_PER_CI = 0.0163871


def a_chord(R, r):
  """Computes the area of a chord as a function of radius, R, and apothem, r."""
  return R**2 * acos(r/R) - r * sqrt(R**2 - r**2)

def v_lo(W, L, z):
  """Computes volume for bottom semicircular region."""
  R = W/2
  return L * a_chord(R, R - z)

def v_mid(W, L, z):
  """Computes volume for region up to bottom of top semicircular region."""
  R = W/2
  return v_lo(W, L, R) + L * W * (z - R)

def v_hi(W, L, z):
  """Computes volume for region up to top of tank."""
  R = W/2
  h2 = H - R
  top = (pi * R**2)/2 - a_chord(R, z - h2)
  return v_mid(W, L, h2) + L * top


if len(sys.argv) < 4:
  print """USAGE: %s length width height
       where units are in inches""" % basename(sys.argv[0])
  sys.exit(0)

try:
  L = float(sys.argv[1])
  W = float(sys.argv[2])
  H = float(sys.argv[3])
except:
  print 'Invalid tank dimensions. Integer or decimal input required.'
  sys.exit(0)

for z in range(1, int(H)+1, 1):
  if z < W/2:
    V = v_lo(W, L, z)
  elif z <= H - W/2:
    V = v_mid(W, L, z)
  else:
    V = v_hi(W, L, z)
  print '%3d in %7.0f gal %8.0f L' % (z, V * GAL_PER_CI, V * L_PER_CI)