Help with applying Vertical coordinate transformation to a terrain dataset in ArcGIS

[ErnestFonyuy]

I  have a 1/3 arc-second DEM terrain data (tif) retrieved  from the national map.

The horizontal coordinates are in degrees and the vertical coordinates are in meters.

I want my horizontal coordinates to be in NAD_1983_StatePlane_Texas_South_Central_FIPS_4204_Feet. So I performed a geographic coordinate projection.

 Now I want my vertical coordinates to be referenced to : NAVD88_height_(ftUS). Should I now just perform a vertical coordinate  projection and my  elevation values will be converted to feet?.  Or do I have to  manually convert using raster calculator after performing the vertical projection?

[DanPatterson]

Project (Data Management)—ArcGIS Pro | Documentation   Features

Project Raster (Data Management)—ArcGIS Pro | Documentation  Rasters

To perform a vertical transformation, check the optional Vertical parameter. By default, the Vertical parameter is inactive and becomes active when the input and output coordinate systems have a vertical coordinate system (VCS) and the input feature class coordinates have z-values. Also, additional data (coordinate systems data) setup must be installed on the system.

When you select the output coordinate system, you can choose the geographic or projected coordinate system and a VCS. If the input and output VCS are different, an appropriate vertical and an optional geographic (datum) transformation are available. If a transformation should be applied in the opposite direction to its definition, choose the entry with the tilde (~) in front of the name.

[ErnestFonyuy]

Hello DanPatterson, 

Thank you for your prompt reply. 

When I perform Geographic coordinate system projection   using NAD_1983_StatePlane_Texas_South_Central_FIPS_4204_Feet, the horizontal coordinates are transformed to feet. Why is it that when I perform vertical Coordinate projection using NAVD88_height_(ftUS), the  elevation units remain in meters and not  convert to meters? Any idea  why?

 My thinking was that once i perform Vertical Projection ,  elevation values will change from meters to feet.