Mathcad Community Challenge May 2025: Spin Gravity

The Challenge

Last month’s Mathcad challenge was based on spin gravity:

Spin gravity is a method of creating the sense of gravity in a low- or zero- gravity environment using rotational movement. During this circular motion, objects with mass feel a fictitious centrifugal force “pushing” them away from the center. This force can feel like the gravity we experience on Earth.

You can either design your own space station / vehicle or choose one (or more) from science fiction books, television shows, movies, video games, or other media. Then create a Mathcad worksheet to calculate the following:

Radius of your spinning object.

• Centrifugal acceleration in both distance units per second squared and g’s (acceleration due to gravity at the earth’s surface). Note that your vehicle / station does not need to be 1g. Less than 1g makes it easier to move. More than 1g would help improve your jump shot on your eventual return to Earth.
• Angular velocity in radians, degrees, and revolutions per time unit. Don’t spin too fast, or you will make people feel sick!
• Tangential velocity.

Optional:

• Incorporate Combo Boxes, Sliders, Check Boxes, Radio Buttons, or any other input controls to allow users to change a parameter to see how it affects other calculations.
• Use XY Plots, 3D Plots, Contour Plots, or Chart Components to depict the acceleration due to gravity as a function of one or more other parameters for a space station / vehicle.

The Submissions

This month we had five submissions from three regular contributors, Fred Kohlhepp, Professor Tetsuro Tokoro, and PPal.

Fred Kohlhepp was the first to submit an entry. I like his worksheet because it reads like a think tank paper that both educates and provides directions towards solutions. There’s great use of text regions, images, XY plots, formatting, and math regions within text regions. The worksheet designs a space station for 200 people in a bicycle wheel design, based in inertia stability studies. For a standard 1g Earth environment, the angular velocity comes out at a comfortable 1.5 RPMs.

There’s a nice XY plot with a logarithmic Y-axis that plots angular velocity as a function of radius, with multiple plots for different values of gravity. There’s also an interesting examination of how pressure on a column of water would vary along the spokes of the bicycle wheel. The worksheet concludes with examining the magnified Coriolis effect of the space station compared to Earth. Very well thought out.

Professor Tokoro, as usual, provided several worksheets, each one building on or creating a variation of the previous. They are all characterized by advanced 3D plotting.

The first worksheet solves the basic calculations for a spinning object of 100 meters radius. Then it has slider controls where users can change radius and angular velocity to see the resulting effect on the spin gravity force. I really like slider controls in conjunction with plots because they help people understand the relationships between variables.

The second worksheet changes the 3D plot to depict the spin gravity force and spinning object radius on a torus. The vectors change size based on the slider inputs. The magnitude of the force even changes the color of one of the vectors! Another 3D plot changes the color of the torus in comparison to Earth gravity. This worksheet also incorporates Combo Boxes and Check Boxes for inputs. People can take their worksheets to the next level by incorporating the 3D plot techniques here.

The third worksheet had Combo Boxes for choosing different accelerations due to gravity and conditions (Earth, Moon, Mars, and Space). Then with a slider to control radius, a 3D plot updates. Mars and the Moon created inverted 3D paraboloids. But honestly, I wasn’t sure what I was looking at. Some additional text boxes would help with comprehension. Regardless, the second worksheet was my favorite and a tour de force in plotting with conditional formatting.

PPal’s worksheet opened with a nice discussion regarding rotation rate, radius of rotation, and artificial gravity level. The worksheet contained slider controls for radius and gravity level. Text boxes had conditional formatting for RPMs (green for acceptable and maximum comfort, yellow for OK with training, and red for unsuitable), gravity gradient, and Coriolis acceleration. The worksheet then analyzed two scenarios for the Coriolis Effect, water pressure spin, and a little bit of structural analysis (cross section required to support a given mass and angular velocity). This worksheet shows the power of advanced controls with conditional formatting for conveying information.

Another Entry

Occasionally I like to submit my own worksheets in the challenge, but I generally don’t write about them. I’m making an exception due to a conversation on PTC Community.

I wanted to investigate the relationships between radius of the spaceship / station and centrifugal acceleration as the independent variables, and angular velocity as the dependent variable. Rotating more than 5 RPM tends to induce nausea in people. This would be a great use of custom unit systems and scripted controls with Python in Mathcad Prime 11.

On PTC Community, David Newman (the organizer of the Mathcad Challenge from PTC) pointed out that it is a best practice to duplicate scripted controls in both JScript and Python. JScript is automatically installed in all Windows operating systems, but users have to install Python manually. If you intend to share your Mathcad worksheets with others, it’s best not to assume that someone has installed Python.

Takeaways

My main takeaway from this challenge, as well as the past few (check the archives!) is that conditional formatting really amps up the power of your worksheet and its ability to communicate. In industry, I’ve seen so many papers and analyses bury their conclusions in text and numbers without context. By combining advanced inputs with plotting and color coded text boxes, you can make sure your reader comes to the conclusion you want them to make.

This was the first challenge after the release of Mathcad Prime 11. In addition to the aforementioned enhancements like custom units systems and scripted controls using Python, there are a lot of other improvements. These include Manual Calculation Mode, Result Threshold Formatting, Slider control min and max values display, the new “vec” function, and support for results formatting in binary, octal, and hexadecimal numbers. You can try the latest version of Mathcad Prime for free here!