I don't have much of a response because I don't think there is much concrete evidence to support the use of these for performance.  Once there is evidence, it is usually manufactured to an extreme.  In cases where anything is found to be extremely effective, then we see a ban by WADA.  

 My recommendation and personal choice - eat real food, and always your veggies, like my Mom taught me. :)

Amen, Laura! Love good food. Eat close to home. Connect with your family in the kitchen, garden, with a CSA, and pyo field trips.

I think we should direct them to Stacy Sims’ work nicely presented in her 2017 book: “ROAR: How to Match Your Food and Fitness to Your Unique Female Physiology for Optimum Performance, Great Health, and a Strong, Lean Body for Life.” What do you think? A good first intro is Tina Muir’s interview with Sims on her podcast, Running 4 Real. I am a fan of Muir’s podcasts!

Also: Dr. Jennifer Gaudiani: Celebrate Body Diversity (very helpful information to diagnose and understand Eating Disorders and Disorder Eating, for athletes, parents, coaches, everyone)

I second that: Tina Muir is great.  

Okay, preface: of all the questions I have offered input on, this is perhaps the one I am least qualified for. That said, I will give an opinion.

Short answer, yes, there has been evidence that both beet juice and turmeric may have positive effects on types of athletic performance and aspects of overall health.

Beet juice (along with many leafy greens) contains a high concentration of nitrate, which is converted into nitric acid within the body, and has a role in regulating blood vessel dilation and mitochondrial biogenesis (essentially, growing stronger mitochondria, the cellular "energy centers," and key players in aerobic output.) Some studies have shown a decrease in systolic blood pressure following several days of consuming beet juice, and studies of high performance endurance athletes show that this may correlate with lower oxygen consumption over a maximal effort session.

What you really want out of turmeric is curcumin, and it takes a lot of turmeric to get the amount necessary for any significant effect. So if you want to go the turmeric route, get a supplement, don't just add the spice to your food. There are various claims and a good bit of evidence for turmeric's ability to help reduce inflammation, contribute to management of conditions such as arthritis and anxiety, and potentially even reduce the risk of cancer.

There are considerations around both nitrate and curcumin supplementation with regard to how to increase absorption into the bloodstream, potential negative interaction with other supplements, and contraindications. Do your research; if you're supplementing, you'll want to give your body a good chance of actually using the thing. And it doesn't hurt to check in with your doc (insert standard disclaimer here.)

As with all supplements, there are extravagant claims in circulation about both of these supplements, as well as conflicting research. The positive effects found in some studies are not guaranteed for any individual athlete nor are nitric acid and curcumin the only ways to achieve the effects they may have. I recommend that any athlete considering adding a supplement get a clear picture of what effect they are hoping this supplement might have, why they are interested in this effect, and what else they could be doing to support this goal. There are many ways to "skin the cat," and the magic pill route functions best as a minor part of an overall healthy picture, which will likely include dietary modifications and consideration to various lifestyle components.

Additionally, athletes may want to experiment and see for themselves. It seems that every elite athlete has their own favorite miracle supplement, so you might want to try a few to find yours... or you might decide it's a waste of time. The decision is yours. As long as your doctor agrees, it's probably a safe bet that drinking beet juice won't hurt you, so you could always just do it for the placebo. Going to some length to achieve an effect (i.e; taking your turmeric to reduce inflammation) may further motivate an individual to adopt other behaviors in support of that same goal, such as reducing refined sugar intake. As with any good experiment, if you do decide to experiment, change one variable at a time: add the supplement, test the specific function this supplement is supposed to improve performance around, and see if you notice a change. If you like it, you can become another athlete raving about their personal favorite supplement.

I have read many articles and books that discuss and recommend natural supplements, or not, and as a result can offer the following takeaway: It’s impossible to prove whether natural supplements are effective or not but, unless you take megadoses of highly concentrated herbs, spices, etc., they will do you no harm. As one author put it, “a medical claim about the effect of a supplement is just that, a claim and not proof.” There is also the placebo effect to consider. The placebo effect is defined as "a beneficial effect produced by a placebo drug or treatment, which cannot be attributed to the properties of the placebo itself, and must therefore be due to the patient’s belief in that treatment.” So, I say, if you think it helps and it’s not too expensive, go with it.

Another important question is, how long has a given natural supplement been around - 10 years, 100, 10,000? Personally, I am much more apt to try a spice or herb that has been a mainstay ingredient in a cultural cuisine in a distinct area of the world for millennia, such as turmeric, aka cumin, has been for India. Unfortunately, today’s herbs and spices are not what they used to be, having been refined and tampered with, so, I think it makes sense to support our local farmers to choose local organically grown whole foods, herbs and spices. 

The bottom line is more about what you don’t eat or add to your food than it is about what you do add. My apologies for circling back to this topic, but, for my money, there are many battles going on within the world of health and nutrition, natural supplements among them but the War needs to be fought on refined carbohydrates. Burn more fat and eat fewer carbs = live lean.

I have always wondered what the attraction for beetroot juice was. So I have been doing some reading since this question was posted. It appears to me that the nitrate levels in your blood respond quickly to drinking beetroot juice, but you actually achieve the same levels, just a bit slower, by eating spinach and lots of other vegetables.

In other words, if you have a race in an hour, and you haven't eaten your veggies all week, then you might think about beetroot juice.  

Admittedly, my research was pretty shallow.