Vectors - Fuel Economy, Hypermiling, EcoModding News and Forum

JulianEdgar · 12-16-2020, 11:16 PM

I keep mentioning vectors here, but people without any physics won't know what I am talking about. But it's really easy - and quite empowering.

A vector, in the way I am using it, describes a force. A force (a push or pull) has a strength and a direction. If we use an arrow, the arrow points in the direction the force is acting, and the length of the arrow shows the strength of the force.

So if we take my Insight, and look at pressures acting over the rear hatch, we can see that the pressures here are all negative - they're pulling, and largely upwards.

So let's look at one of those 'pulling pressures' on the hatch - say -80 (ie minus 80 - less than atmospheric).

Now, all pressures act at right-angles to the panel, so let's draw in the panel angle:

...and then the vector (the force direction and magnitude) at right-angles to the panel:

Now it gets really exciting. How much lift and drag is this force causing? We can find that out by using the 'triangle of forces':

Here the green line shows the magnitude and direction of lift resulting from the -80 pressure, and the blue line shows the direction and magnitude of the drag resulting from the -80. (I could have added arrow heads to these - upwards for the lift force and backwards for the drag force).

You can use math geometry to work out the actual ratios of the forces, or just draw it to scale (as I did on a bit of paper). That shows the ratio of lift:drag for any low pressure on the Honda's hatch is about 100:15, or each 100 units of lift has 15 units of drag.*

So if I increase pressures on the hatch, as I have done with my rear spoiler, that same ratio applies for reducing lift and drag.

Now to work out the actual forces involved, we need to multiply the pressures by the areas, and then do our triangle of forces for each. So it's certainly not an easy way of working out total drag changes, but it very clearly shows where the drag (and thrust too of course - look at the -34 at the nose) forces are occuring.

*That's actually very conservative - as shown in the diagram above, it's a bit higher (ie steeper 'best fit' angle line).

JulianEdgar · 12-16-2020, 11:16 PM

One more point. As the rear spoiler on the Insight is made higher, so the pressures in front of it will increase (ie reducing lift and drag). But the spoiler is creating its own drag, so for lowest drag, it's one thing fighting the other.

In a video I have coming up on my YouTube channel, I show a Porsche diagram that Dr Wolf was kind enough to give me (I sent him some pics and a description of the Insight rear spoiler) that precisely shows the trade-off of different height spoilers on a 911 model - drag versus lift... and yes, there is a sweet spot.