How is the climb gradient calculated? I was part of a discussion about the differences between all engine climb gradients and one engine inoperative (OEI) climb gradients, and a colleague suggested that climb gradient can be calculated as 

$G = \frac{T-D}{W}$

Where 


$G$ is Climb Gradient as a percent,
$T$ is Thrust, 
$D$ is Drag, and 
$W$ is Weight.


This derivation was never really explained, and it doesn't really make sense to me.  He continues by stating that lift can be assumed to equal weight for small climb angles, so that his equation becomes 

$G = \frac{T}{W} -\frac{D}{L}$

Where $L$ is Lift.

For some analyses, I can see using the approximation $W = L$, but since that is essentially assuming your climb gradient is 0, it doesn't seem prudent to use that assumption to calculate the climb gradient itself.

Has anyone seen these equations before?  Or is there a piece to this that I'm missing that someone could explain to me?
Assuming that thrust is entirely in the direction of travel and the flight path angle is constant, the Lift is equal to the weight times the cosine of the flight path angle:

$L = W\cos(\gamma)$

For small $\gamma$, $\cos(\gamma) \approx 1$

E.g. for a flight path angle of 10 degrees, the error introduced by the approximation is ~ 1.5%



For unaccelerated climb, the sum of all forces in the along path direction cancel each other out:

$ T-D-W\sin(\gamma) = 0$

The gradient is $\tan (\gamma)$.

Again, for small angles, $\sin(\gamma)\approx\tan(\gamma)$

From there it is a small step to see that the calculation suggested by your colleague is acceptable for unaccelerated climbs at small flight path angles.