# Can GPS signals penetrate steel in the thickness of few centimeters?

Can GPS signals penetrate steel in the thickness of few centimeters?

Can they penetrate even thicker steel or other materials than steel (as well as steel?)?

• My GPS stops working if I move it to the centre of the car i.e. as far as possible from the windows. That suggests the mm or so of steel in my car is enough to stop the GPS signal. Commented May 6, 2017 at 7:17

If you have a look at my answer to http://physics.stackexchange.com/questions/160137/faraday-cage-in-real-life?lq=1 you will see I give a relatively simple formula for transmission of an EM wave (at radio or microwave wavelengths) through a sheet of metal. $$\frac{E_t}{E_i} \simeq 4 \frac{\eta_{\rm Fe}}{\eta_0} \exp(-t/\delta) ,$$ where $t$ is the thickness and $\eta_{\rm Fe}$ is the (complex) impedance of the steel, with a magnitude given roughly by $\eta_{\rm Fe} = (\mu_r \mu_0 \sigma / \omega)^{1/2}$, where $\omega$ is the angular signal frequency, and $\mu_r=1000$ and conductivity $\sigma= 2 \times 10^{6}$ S/m are reasonable values for steel, $\eta_0 =377\Omega$ is the impedance of vacuum, and $\delta \sim (2/\mu_r \mu_0 \sigma \omega)^{1/2}$ is the skin depth of a good conductor. The first term in the product is caused by reflection from the steel, the second term is caused by dissipation of the wave as it travels in the steel. The transmitted power fraction would be the square of this.
GPS signals work at about 1.5 GHz, so $\omega \sim 10^{10}$ rad/s, $\delta \sim 3\times 10^{-7}$ m (which already tells you the answer) and $\eta_{\rm Fe} \sim 5\times 10^{-4}\Omega$. The fraction of the E-field at that frequency that is not reflected from a steel surface is already down at $2\times 10^{-6}$ and the fraction that transmits a cm of steel is smaller than can be accommodated on my calculator. A very thin steel foil would block a GPS signal.
Obviously, GPS can penetrate other (non-conducting) materials, like glass and air for instance. It can also penetrate conducting frameworks, so long as the openings in the framework are much larger than the wavelength of $\sim 20$ cm. The windows of a car are therefore an intermediate case.