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The Physics Behind Tesla’s Flying Roadster

We’ve been promised flying cars for decades. We finally have one. Well, sort of. Last week, Elon Musk revealed Tesla’s long-delayed Roadster 2 with a few bells and whistles. The car flies—but not for very long—and the prototype also did a few other things normal cars can’t, like driving up a vertical wall and jumping over Tesla’s entire lineup of vehicles.

几十年来，我们一直被承诺会有飞行汽车。现在我们终于有了一辆。好吧，算是吧。上周，埃隆·马斯克发布了特斯拉迟迟未出的 Roadster 2，并增加了一些花哨的功能。这辆车可以飞行——虽然时间不长——而且原型车还展示了普通汽车做不到的其他事情，比如垂直爬墙以及跳过特斯拉的整个产品阵容。

This raises two questions: Should we let humans drive up walls and into the air? Given their trouble navigating two-dimensional roads, this seems like an obvious no. But that’s one for lawyers and the Federal Aviation Administration to figure out. The other question is, how did the Roadster 2 prototype do this stuff? We can answer that ourselves, with physics.

这引发了两个问题：我们应该允许人类开车爬墙和飞向空中吗？考虑到人类在二维道路上行驶都困难重重，答案显然是不应该。但这需要律师和联邦航空管理局去解决。另一个问题是，Roadster 2 原型车是如何做到这些的？我们可以用物理学来回答这个问题。

Driving Up a Wall: Let’s start with how the car drove up a circular ramp and then stayed glued to it Spider-Man–style, completely upside down. I don’t think you should ever do this, but this feature of the Roadster 2 can actually improve performance on normal roads. It has to do with friction.

爬墙：让我们从这辆车如何驶上圆形坡道，然后像蜘蛛侠一样完全倒挂在上面说起。我不认为你应该尝试这样做，但 Roadster 2 的这一功能实际上可以提高在普通道路上的性能。这与摩擦力有关。

When two surfaces interact—like rubber tires and a road—there can be a force that prevents the surfaces from sliding relative to one another. This interaction is called static friction. We have a simple model for this static friction force where the magnitude (Ff) depends on how hard the two surfaces are pushed together (FN) and the two types of surfaces (μ).

当两个表面相互作用时——比如橡胶轮胎和路面——会产生一种阻止表面相对滑动的力。这种相互作用被称为静摩擦力。我们有一个简单的静摩擦力模型，其大小 (Ff) 取决于两个表面被挤压的力度 (FN) 以及两种表面的类型 (μ)。

The force pushing the surfaces together is often called the “normal” force, since it’s perpendicular to both surfaces. The coefficient of static friction (μ) describes the types of materials interacting. The practical maximum coefficient of friction is 1, and for rubber on asphalt, the value is somewhere around 0.6. What about that ≤ sign? This is because static friction is a “force of constraint.” It applies the force needed to prevent sliding—up to some maximum value.

将表面挤压在一起的力通常被称为“法向力”，因为它垂直于两个表面。静摩擦系数 (μ) 描述了相互作用的材料类型。实际的最大摩擦系数为 1，对于沥青路面上的橡胶，该值约为 0.6。那个 ≤ 符号是怎么回事？这是因为静摩擦力是一种“约束力”。它施加必要的力来防止滑动，最高可达某个最大值。

Suppose a mere mortal car tries to drive up an incline. Here’s a force diagram showing the three important forces: friction, normal force, and gravity (the product of mass and the gravitational field). As the angle (θ) of the incline increases, the gravitational force (mg) has less of a component in the direction perpendicular to the surface. This means the normal force (FN) also decreases, as does the maximum frictional force. If this frictional force is less than the component of the gravitational force pulling down the incline, the car will slip. With a coefficient of 0.6, this maximum angle is about 31 degrees. That’s not vertical. It’s not even close to vertical. Even with a coefficient of friction at 0.9, you still only get to an incline of 42 degrees.

假设一辆普通的汽车试图驶上斜坡。这里有一张力学图，显示了三个重要的力：摩擦力、法向力和重力（质量与重力场的乘积）。随着斜坡角度 (θ) 的增加，重力 (mg) 在垂直于表面方向上的分量会减小。这意味着法向力 (FN) 也会减小，最大摩擦力也随之减小。如果这个摩擦力小于重力沿斜坡向下的分量，汽车就会打滑。在系数为 0.6 的情况下，这个最大角度约为 31 度。这并非垂直。甚至离垂直还差得远。即使摩擦系数达到 0.9，你也只能达到 42 度的斜坡。

So how can a car drive up a vertical wall? The answer is to increase the normal force—and, by extension, the frictional force. For a vertical wall, this friction force must be equal to the gravitational force to prevent the car from slipping. Here’s where the Roadster 2 does its first trick. It uses fans to blow air out from under the car. With some side flaps, this lowers the air pressure under the car, akin to how a vacuum cleaner works.

那么汽车如何才能驶上垂直墙壁呢？答案是增加法向力，进而增加摩擦力。对于垂直墙壁，这种摩擦力必须等于重力，以防止汽车下滑。这就是 Roadster 2 的第一个技巧所在。它利用风扇将车底的空气吹出。配合侧面的襟翼，这会降低车底的气压，类似于吸尘器的工作原理。

Just for fun, let’s estimate the pressure under the Roadster 2 that you would need for it to stick to a wall. The company says the car has a target weight of 1,700 kilograms. We also need to know the contact area. Let’s ballpark it at around 2 square meters. Remember that F = P × A, where P is the pressure and A is the area. But this is really a pressure difference with the external atmospheric pressure at about 105 newtons per square meter. Cranking the numbers gives a bottom pressure of 86 percent of atmospheric pressure. That seems very plausible. Of course, since the seal around the bottom isn’t perfect, the fans will need to continue pulling out.

为了好玩，让我们估算一下 Roadster 2 要吸附在墙上所需的车底压力。该公司称该车的目标重量为 1,700 公斤。我们还需要知道接触面积。我们粗略估计为 2 平方米左右。记住 F = P × A，其中 P 是压力，A 是面积。但这实际上是与外部大气压（约 105 牛顿/平方米）之间的压差。计算得出车底压力为大气压的 86%。这看起来非常合理。当然，由于车底周围的密封并不完美，风扇需要持续抽气。

The upside-down Roadster 2 makes for a compelling sales pitch, but the suction actually has a strong use case when it’s driving right side up. Frictional force is the thing that makes a car accelerate. More frictional force, better performance. Pushing the car down means you can accelerate faster and brake faster and make sharper turns. (Performance automakers have harnessed this principle for decades, though not to the degree of Tesla’s new prototype.)

倒挂的 Roadster 2 是一个引人注目的卖点，但这种吸力在汽车正常行驶时也有很强的应用价值。摩擦力是汽车加速的关键。摩擦力越大，性能越好。将车身向下压意味着你可以加速更快、刹车更灵敏，并进行更急的转弯。（高性能汽车制造商几十年来一直利用这一原理，尽管程度不及特斯拉的新原型车。）

0–60 in 1 second: The Roadster 2 also boasts an acceleration of 0 to 60 mph in less than a second. For a traditional car, this is impossible. Since a normal car uses the frictional force between the tires and road to accelerate, it’s limited by the coefficient of friction. Using a coefficient of friction at 0.6 (reasonable), the best you can do is 0 to 60 mph in 4.56 seconds. Yes, you can get better tires and you can also increase the frictional force once the car moves faster and interacts with the air (pushing it down)—but those improvements still won’t get you to 60 mph in a second.

0 到 60 英里/小时加速仅需 1 秒：Roadster 2 还宣称 0 到 60 英里/小时的加速时间不到一秒。对于传统汽车来说，这是不可能的。由于普通汽车利用轮胎与路面之间的摩擦力来加速，它受到摩擦系数的限制。使用 0.6 的摩擦系数（合理的数值），你所能达到的最好成绩是 4.56 秒内从 0 加速到 60 英里/小时。是的，你可以换更好的轮胎，也可以在汽车加速并与空气相互作用（向下压）时增加摩擦力，但这些改进仍然无法让你在 1 秒内达到 60 英里/小时。

The Roadster 2 relies on another form of force: compressed air shooting out the back. This is how rockets work. Since most of us don’t have rockets handy, consider the simple experiment of a toy car propelled by an inflated balloon. Once the balloon is released, the stretched rubber acts as a force that pushes the air out of the balloon and through an attached tube. But since this air has mass, it will take a force to accelerate it from rest to its exhaust velocity. Here’s the cool thing about forces—they are an interaction between two things (like the balloon and the air). That means that when the balloon’s walls push on the air, the air pushes back with an equal force in the opposite direction—an example of Newton’s third law. This push-back force on the balloon is what makes the toy car accelerate. Instead of a wheezing balloon, the Roadster 2 relies on a tank of compressed air.

Roadster 2 依赖于另一种形式的力：从车尾喷出的压缩空气。这就是火箭的工作原理。由于我们大多数人手头没有火箭，可以考虑一下由充气气球驱动的玩具车这个简单的实验。一旦气球被释放，拉伸的橡胶就会产生一种力，将空气从气球中挤出并通过连接的管子。但由于这些空气有质量，需要一个力才能将其从静止状态加速到喷射速度。关于力，最酷的一点是它们是两个物体之间的相互作用（比如气球和空气）。这意味着当气球壁推动空气时，空气会以相等的力向相反方向推回——这是牛顿第三定律的一个例子。这种对气球的反作用力就是让玩具车加速的原因。Roadster 2 不再使用漏气的气球，而是依赖一个压缩空气罐。

Flying Cars (Sort Of): Now, we get to the flying car part. The Roadster 2 uses the same compressed-air method to push up on the car and get it off the ground. That’s stretching the limits of the term “flying,” especially because there’s only a few seconds of thrust that

飞行汽车（算是吧）：现在，我们谈谈飞行汽车的部分。Roadster 2 使用同样的压缩空气方法来向上推动汽车，使其离开地面。这有点延伸了“飞行”一词的定义，特别是考虑到只有几秒钟的推力……