How Deep is Challenger Deep?

It’s about 8 Saarlands to the Wales.

What I’ve never understood is how many double decker buses fit in an olympic-size swimming pool. Or why journalists use analogies that are impossible to grasp, without also giving the numbers. (I think I have maybe seen one olympic swimming pool in my entire life? so I have no idea how much water they hold. And it varies because the depth isn’t strictly standardized. I only know the size of a double decker bus (a routemaster, not a modern bus) from a Flanders and Swann song.)

Previously elsewhere…

https://press.asimov.com/articles/metaphors-size

https://chaos.social/@weirdunits

https://youtu.be/sdWEGzWFcCc

(Brits don't call soccer "soccer" they call it "football", which is far more ambiguous, and it upsets rugby fans, so I like to annoy soccer fans by calling it soccer, and to annoy rugby fans by asking "league or union", because I genuinely have no idea and they of course feel that I should.)

I did actually swallow my pride and wrote “Soccer” because it’s internationally unambiguous and we’re inclusive here, but it’s also a sin that rests heavy on my soul that I called it this way ;).

I wonder if there is a Wales-to-Saar-region converter? :-)

Let’s see what I do for Christmas.

It’s a page showing off a bit from a geovisualisation company. I think it’s okay to show some splendour.

It looks like the terminal velocity is about 2.1 m/s in seawater. Interestingly enough, the change in water density is negligible over the 11 km drop.

The overall time will depend on the shape of the rock and its density, but it should take about 90 minutes (give or take) to reach the bottom.

Here is a simple python script to simulate the drop:

import numpy as np
import matplotlib.pyplot as plt

# ---------------------------
# Physical parameters
# ---------------------------

rho0 = 1025                    # seawater density at surface (kg/m^3)
beta = 4.5e-10                 # density increase per meter
rho_r = 2700                   # rock density (kg/m^3)
g = 9.81
Cd = 0.47                      # drag coefficient for a sphere

r = 0.05                       # 10 cm diameter -> radius 5 cm
V = (4/3)*np.pi*r**3
A = np.pi*r**2
m = rho_r * V

def rho_water(z):
    return rho0 * (1 + beta * z)

# ---------------------------
# Time integration setup
# ---------------------------

dt = 0.01                      # time step (s)
z = 0.0                        # depth (m)
v = 0.0                        # velocity (m/s)
t = 0.0                        # time (s)

z_list = []
v_list = []
t_list = []

# ---------------------------
# Integrate until 11 km depth
# ---------------------------

while z < 11000:
    rho = rho_water(z)

    # Forces
    F_gravity  = m * g
    F_buoyancy = rho * V * g
    F_drag     = 0.5 * rho * Cd * A * v * abs(v)

    # Net force
    F_net = F_gravity - F_buoyancy - F_drag

    # Acceleration
    a = F_net / m

    # Update motion
    v += a * dt
    z += v * dt
    t += dt

    # Save for plotting
    z_list.append(z)
    v_list.append(v)
    t_list.append(t)

# ---------------------------
# Results
# ---------------------------

print(f"Time to reach 11,000 m: {t/60:.2f} minutes ({t:.1f} seconds)")
print(f"Final velocity: {v:.3f} m/s")

# Optional: plotting
plt.figure(figsize=(10,4))
plt.subplot(1,2,1)
plt.plot(t_list, z_list)
plt.xlabel("Time (s)")
plt.ylabel("Depth (m)")
plt.title("Depth vs. Time")

plt.subplot(1,2,2)
plt.plot(t_list, v_list)
plt.xlabel("Time (s)")
plt.ylabel("Velocity (m/s)")
plt.title("Velocity vs. Time")

plt.tight_layout()
plt.show()