Until now it has been impossible to observationally measure how star cluster scale height evolves beyond 1 Gyr as only small samples have been available .
Here we establish a novel method to determine the scale height of a cluster sample using modelled distributions and Kolmogorov-Smirnov tests .
This allows us to determine the scale height with a 25 % accuracy for samples of 38 clusters or more .
We apply our method to investigate the temporal evolution of cluster scale height , using homogeneously selected sub-samples of Kharchenko et al .
( MWSC ) , Dias et al .
( DAML02 ) , WEBDA , and Froebrich et al .
( FSR ) .

We identify a linear relationship between scale height and log ( age / yr ) of clusters , considerably different from field stars .
The scale height increases from about 40 pc at 1 Myr to 75 pc at 1 Gyr , most likely due to internal evolution and external scattering events .
After 1 Gyr , there is a marked change of the behaviour , with the scale height linearly increasing with log ( age / yr ) to about 550 pc at 3.5 Gyr .
The most likely interpretation is that the surviving clusters are only observable because they have been scattered away from the mid-plane in their past .
A detailed understanding of this observational evidence can only be achieved with numerical simulations of the evolution of cluster samples in the Galactic Disk .

Furthermore , we find a weak trend of an age-independent increase in scale height with galactocentric distance .
There are no significant temporal or spatial variations of the cluster distribution zero point .
We determine the Sun ’ s vertical displacement from the Galactic Plane as Z _ { \odot } = 18.5 \pm 1.2 pc .