File:Allometric Law of Body Mass vs Cruising Speed in Constructal Theory.svg

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Summary

Description
English: The proportionality between the optimal cruising speed for flying bodies (insects, birds, airplanes) and body mass in kg raised to the is an allometric law predicted by Konstruktalteori:
Español: La proporcionalidad entre la velocidad óptima de crucero para los cuerpos voladores (insectos, aves, aviones) y el cuerpo de masa en kg planteadas a la es una ley alométrica predicha por Konstruktalteori:
Svenska: Proportionaliteten mellan den optimala marschfarten för flygande kroppar (insekter, fåglar, flygplan) och kroppsmassa i kg upphöjt till är en allometrisk lag förutsagd av Konstruktalteori:
Date
Source Own work
Author Nicoguaro

This file was created with Python,NumPy and Matplotlib.

from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams

rcParams['font.family'] = 'serif'
rcParams['font.size'] = 12

# Data
masses = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(0,))
speeds = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(1,))
names = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(2,), dtype=str)
groups = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(3,), dtype=str)
posx = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(4,), dtype=int)
va = np.loadtxt("Allometric_law.csv", skiprows=1, delimiter=",",
                  usecols=(5,), dtype=str)
x_vals = np.logspace(-5, 6)
y_vals = 30*x_vals**(1./6.)

# Big plot
fig = plt.figure(figsize=(15, 10))
ax = plt.subplot(111)
box = ax.get_position()
ax.set_position([box.x0, box.y0, box.width, 0.7*box.height])
plt.plot(x_vals, y_vals, "k", zorder=3, alpha=0.4)
plt.loglog(masses, speeds, "ko", zorder=5)
plt.xlabel("Mass (kg)")
plt.ylabel("Speed (m/s)")
plt.yticks([1, 10, 100, 300], [1, 10, 100, 300])
plt.ylim([1, 300])
for cont in range(len(masses)):
    mass = masses[cont]
    speed = speeds[cont]
    name = names[cont]
    if va[cont] == "top":
        pos = (posx[cont], -10)
    else:
        pos = (posx[cont], 10)
    plt.annotate(name, xy=(mass, speed), xytext=pos,
        textcoords="offset points", ha="center", va=va[cont],
        rotation="vertical", backgroundcolor="white", zorder=4,
        fontsize=10)

# Small plot
ax2 = plt.axes([.2, .6, .4, .32])
plt.loglog(masses[groups=="Insects"], speeds[groups=="Insects"],
           marker="o", mfc="white", lw=0)
plt.loglog(masses[groups=="Birds"], speeds[groups=="Birds"],
           marker="s", mfc="grey", lw=0)
plt.loglog(masses[groups=="Airplanes"], speeds[groups=="Airplanes"],
           marker="^", mfc="black", lw=0)
plt.annotate("Insects", xy=(2e-5, 2))
plt.annotate("Birds", xy=(0.2, 4))
plt.annotate("Airplanes", xy=(4e3, 40))
plt.xticks([1e-5, 1, 1e5], [r"$10^{-5}$", r"$1$", r"$10^{5}$"])
plt.yticks([1, 10, 100], [r"$1$", r"$10$", r"$100$"])
plt.xlabel("Mass (kg)", fontsize=10)
plt.ylabel("Speed (m/s)", fontsize=10)
plt.ylim([1, 300])

plt.savefig("Allometric_Law_of_Body_Mass_vs_Cruising_Speed_in_Constructal_Theory.svg")
plt.show()

The datafile (Allometric_law.csv) is presented in te table below. The last two columns contain data related to the alignment of the text in the image.

Mass (kg) Speed (m/s) Animal Group Horizontal alignment Vertical alignment
0.0000109 3.9731 House fly Insects 5 top
0.0000491 6.24218 Meat fly Insects 2 bottom
0.0000715 6.91698 Honey bee Insects 2 top
0.000165265 5.86246 Hornet Insects 2 bottom
0.000212458 7.05465 Bumblebee Insects 2 top
0.000715394 6.35818 Dung beetle Insects 2 bottom
0.00309677 7.96499 Ruby-throated hummingbird Birds 2 bottom
0.00398107 5.6114 Goldcrest Birds 2 top
0.00919679 5.84334 Magnolia warbler Birds 0 bottom
0.0108734 7.63583 House wren Birds 3 top
0.0145759 5.60548 Sand martin Birds 2 bottom
0.0195393 6.34111 Barn swallow Birds 2 top
0.0284804 8.63321 House sparrow Birds 2 bottom
0.0309677 6.88293 Skylark Birds 2 top
0.0919679 9.75921 Blue jay Birds 2 bottom
0.251189 8.98027 Sparrow hawk Birds 2 top
0.415128 15.3328 Partridge Birds 2 bottom
0.777874 12.4731 Peregrine falcon Birds 2 top
1.23285 18.4383 Pheasant Birds 2 bottom
1.39783 9.94023 Blue heron Birds 2 top
2.12458 12.7222 Black vulture Birds 2 bottom
3.09677 16.9678 Gannet Birds 0 top
3.51119 13.2516 White stork Birds 7 bottom
4.90805 13.5236 Golden eagle Birds 2 top
5.80278 22.6257 Canada goose Birds 2 bottom
9.19679 18.7912 Wandering albatross Birds 2 top
12.3285 20.824 Mute swan Birds 2 bottom
1042.75 45.3753 Piper Warrior Airplanes 2 top
1519.91 49.2557 Beech Bonanza Airplanes 2 top
1953.93 56.881 Beech Baron Airplanes 5 top
4151.28 64.3216 Beech King Air Airplanes 2 top
7153.94 85.7753 Leerjet 31 Airplanes 2 top
12328.5 107.532 F-16 Airplanes 2 top
20374.7 121.624 Mig-23 Airplanes 2 top
45138.3 199.233 Fokker F-28 Airplanes -5 top
55648.6 131.958 F-14 Airplanes 2 top
58027.8 220.793 Boeing 737 Airplanes 10 top
145759 234.687 Airbus A310 Airplanes 2 top
273126 244.429 Douglas DC-10 Airplanes 2 top
415128 249.429 Boeing 747 Airplanes 2 top


Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution
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  • to share – to copy, distribute and transmit the work
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