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Lesson 7: Applying Construction to Vehicles
Overview
Prerequisites
Along with completing all the lessons up to 6 as well as the box and cylinder challenges, before starting this lesson you will be required to complete the 25 wheel challenge as well.
About your tools
Up until lesson 5, I've been very adamant drawing everything freehand, with felt tip pens, and so on. And this has been for a good reason  it's important to maintain a certain degree of the right kinds of challenges to ensure that you guys gain as much as you can from each lesson.
This lesson, however, is going to be a little different. I am allowing, and in fact encouraging the use of the following:

Ballpoint pen for your linework (don't switch pens to do any sort of "cleanup" pass  use the same pen through all your lines, including construction/box subdivision/etc)

Brush pens for filling in large areas with solid black

Rulers/straight edges for drawing precise construction lines

Ellipse guides for constructing and aligning your ellipses

French curves for any complex, curving lines
Whenever drawing freehand, I still want you to apply the methodology I've outlined in the past  the ghosting method, drawing through ellipses, and so on. That said, in this case it is inevitable that with all of the necessary construction lines, and the significance placed on precision, it's important for you to be able to use tools that will allow you to focus more on the meat of the lesson, which is really about the manipulation and construction of complex compound forms.
As before, do not use pencil or digital media.
Introduction
NOTE ABOUT THE VIDEO: In the intro video I mention that you can use a ballpoint pen to lay down your basic guidelines, then switch to a fineliner. Instead I want you to stick to one kind of pen (ballpoint pens are better in this case), and NOT switch to a different pen type halfway through.
Now we're moving onto vehicles  the last of the dynamic sketching lessons, as far as I've planned. This lesson is very similar to the last one, the only difference being scale. It's definitely an interesting experience, drawing these subjects from life  especially the first two: trains and tanks. Wrapping your head around an object so much larger than you can be tricky at times, and it makes for great practice.
Repeating measurements in space
In the previous lesson, we talked about how we can find the center of a plane in perspective, and use that to subdivide it in a number of ways.
You can also use the reverse of this concept to take a measurement you already have and repeat it back or forwards in perspective (very handy for placing wheels). Since we know that the diagonals of a plane will intersect at its center, you can treat two planes that are sidebyside and equal in length as being two halves of the same plane (I'll refer to it as the compound plane).
Knowing this, if you have a centerline running through them in one dimension, the center of this 'compound plane' lies at the point of intersection of that center line with the line that separates the two individual planes.
To copy the measurement over, just draw a diagonal from the corner of your plane through that midpoint of the opposite edge, as shown here.
Creating a square in perspective
People ask about this every now and then, and it isn't until this point that I'd actually feel it appropriate to teach this technique (although it is referenced in the cylinder challenge as well).
Basically, you can construct a proportional square in 3D space relative to two perpendicular vanishing points (that is, vanishing points whose sets of lines are perpendicular to one another)  it's just a downright pain, especially if you don't have an ellipse guide.

Start out with two perpendicular planes set edge to edge, forming a corner. Leave the far ends of these planes open, as we haven't yet determined their lengths.

Pick one of these planes to turn into a square  you can do the other one afterwards by applying the same steps. In this chosen plane, draw an ellipse.

This ellipse must meet two criteria  first, its minor axis (the line that cuts it into two equal, symmetrical halves down its narrower span) must align to the same vanishing point as the other plane. Not the plane it's on, that's a common mistake. Secondly, the points at which the ellipse contacts the two parallel lines of its enclosing plane must align towards the third vanishing point (which in this case is the vertical one).

Assuming that these criteria have been met, then this ellipse represents a proper circle in 3D space, and therefore any plane enclosing it will represent a square. You can go ahead and close off your plane so the final edge just touches the exposed side of the ellipse  you may need to extend the other edges, as I've done here.
Now there's nothing stopping you from applying these steps to the other plane once you've handled the first. With those two planes properly set up as squares, you've essentially got everything you need to create a cube, and from there you can apply the repeating measurements technique above to extend that cube to whatever set proportions you like.
If you especially enjoy drawing vehicles, you may want to check out the following lessons from Charles Hu's Dynamic Sketching course on our sponsor, New Masters Academy:

In this lesson, Charles explores the elements of cars (with a particular focus on the classics), from their proportions, to their structural components, including their wheels.

With a particular focus on tanks, Charles examines the ways in which they differ from one another, and the structures of their wheels, treads, and other common components in heavy duty military vehicles.

From classic biplanes to sleek fighter jets, Charles explores their structure and how we can use markers, and white pastel pencils/gel pens to build up texture on their rendered surfaces.
In addition to these lessons, you may also want to check out the following from Erik Olson's Linear Perspective Master course:

In the latter half of this lengthy lesson, Erik explores a race car and a blimp with a heavy focus on technical perspective, leveraging orthographic plans and proportional studies, and using them to build up solid, precise, and accurate structures within a shared scene.
Sign up to New Masters Academy with the coupon code DRAWABOX22 — you'll get a full 35% off your first billing cycle.
Homework and exercises
Before starting the homework, be sure to go through all of the demonstrations included in this lesson. I strongly recommend drawing along with them as well and following them closely when doing so.
Also, remember that this homework must be drawn from reference. When looking for reference, I recommend that you specifically look for those of a higher resolution. Google's image search tools allows you to limit your search to large images, and I recommend you take advantage of this. It also wouldn't hurt to do a few studies from life (at least when tackling cars). You may even want to see if you've got any kind of museums near by that feature relevant objects.
The homework assignment for this section is as follows:

1 page of form intersections from lesson 2.

1 page of cylinders in boxes, along with the errorchecking method. You may do these with an ellipse guide.

4 pages of formintersection vehicles. These are purely constructional, approach them as you might the form intersections from lesson 2, by drawing primitives (boxes, cylinders, etc). Focus on drawing through your major geometric forms. you can break them down as far as you like, but remember that we're not interested in the smaller details  just on laying down the primitive forms in the arrangement of a vehicle.

8 pages of vehicles. Mix it up  you don't just have to do things with wheels. Boats, planes, wagons, space ships, etc. are more than welcome. As long as it is used as transport and is large enough to hold a human being within it, it's fair game.
You are welcome to use an ellipse guide, a ruler, and a ballpoint pen if you wish. No pencil or digital media, and stick to one kind of pen for your linework (though a brush pen can be used to fill in large dark areas if appropriate).
Ellipse Master Template
This recommendation is really just for those of you who've reached lesson 6 and onwards.
I haven't found the actual brand you buy to matter much, so you may want to shop around. This one is a "master" template, which will give you a broad range of ellipse degrees and sizes (this one ranges between 0.25 inches and 1.5 inches), and is a good place to start. You may end up finding that this range limits the kinds of ellipses you draw, forcing you to work within those bounds, but it may still be worth it as full sets of ellipse guides can run you quite a bit more, simply due to the sizes and degrees that need to be covered.
No matter which brand of ellipse guide you decide to pick up, make sure they have little markings for the minor axes.