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The phrase "a forward direction" is correct and usable in written English.
It can be used when discussing movement, progress, or orientation towards a specific point or goal.
Example: "In order to achieve our objectives, we must always strive to maintain a forward direction in our planning."
Alternatives: "an onward direction" or "a progressive direction".
Exact(43)
Unconsciousness II was my signal to get moving, and in a forward direction.
When the posterior sucker is released, a wave of contraction of the longitudinal muscles moves in a forward direction; this completes one cycle.
Then, echoing the police version of the shooting, he said he saw Mr. Busch "lunging in a forward direction" toward the officers with his hammer over his head.
Mr. Norman went on to say that "if people are preventing things from moving in a forward direction, they should be replaced".
This power loss, called the friction horsepower, can be evaluated by "motoring" the engine (driving it in a forward direction) with a suitable dynamometer when no fuel is being burned.
In a glass box on the second story of a gleaming shopping mall, the upscale restaurant draws a sophisticated mix of local and European couples for dishes that take indigenous flavors in a forward direction.
Similar(17)
Push the wheels forward by keeping hold of the rims and moving them in a forwards direction.
From them, she absorbed the impression that the "only option for a creative person was constant motion — a lifetime of busy whirligigging in a generally forward direction, until you couldn't do it any longer".
Most people I know live their lives moving in a constant forward direction, the whole time looking backward".
However, because this algorithm moves in a single forward direction, it is 'short-sighted' leading to solutions that are likely to be suboptimal (cf. the maximize 'short-term gain' and 'minimize short-term loss' heuristics [7]).
Red light normally scatters in sound tissue in a predominantly forward direction with minimal light being backscattered.
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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