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The phrase "a certain height of" is correct and usable in written English.
It can be used when referring to a specific but unspecified height in various contexts, such as measurements or descriptions.
Example: "The bridge was designed to accommodate a certain height of vehicles passing underneath."
Alternatives: "a specific height of" or "a particular height of".
Exact(2)
This paper presents a study into the monotonic lateral loading behavior of tetrapod piled jacket foundations in undrained clay, with the complex lateral loads being simplified to an equivalent lateral load acting at a certain height of the jacket.
However, we observed, at zones of the stem disc with a highly reticulate transport system, that some vessels were part of a certain wood patch at a certain height of the tree but were part of wood volumes that were non-existing at this height, only a few hundred micrometers higher in the tree.
Similar(58)
"It set the bar at a certain height for the rest of the film".
This is x, this is the height of the roller coaster, but at every x there's a certain height so y is the function of x and it looks like this.
One they reach a certain height, members of the next generation are too intimidated by their predecessors to strike out on their own (75 76).
As Salmon (1989, p.47) puts it, "a flagpole of a certain height causes a shadow of a given length and thereby explains the length of the shadow".
Typical features are onset within 24 hours of reaching a certain height with the appearance of a usually bilateral and dull headache with a duration of less than one day [12, 44].
But after a certain height, the force of gravity becomes too much, and this flow peters out.
A single Dallas Cowboys football game uses up as much electricity as the entire nation of Liberia in those same three hours -- one reason the globe, if looked at from a certain height, is a cluster of lights surrounded by enormous patches of dark.
Fluid rope coiling, in which a coiling motion of viscous fluid is poured onto a horizontal plane from a certain height with the shape of a thin rope, is known to be one such motion.
For control of the blinds, the control of the upward/downward movement of the blinds, movement of the blinds to a certain height and change in the inclination of the blind slats were tested.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com